Good morning everyone. We give you the most A warm welcome to the Workshop of Mathematics, an academic field that It is part of the sixth workshop in Basic Sciences of the School of Basic Sciences, Technology and Engineering at the National University Open and Distance Learning, UNAP. This space is designed for strengthen mathematical skills and promote understanding of the mathematics as a discipline fundamental for interpretation and formation of the world around us. This In this session we will address three great moments. A conference international that will show us how the Geometry and physics are hidden behind of everyday phenomena. a national conference that will take us through the fascinating universe of robotics and the programming and finally the participation of our youth workers from the Matinova seedbed. We appreciate the participation of our speakers guests, as well as students and teachers who are with us on this day today. We begin our conference international title Why are bubbles always round? The secret of nature to save energy. We are accompanied by Dr. Jorge Octavio Mata Ramírez de la Autonomous University of Baja California, Mexico. Dr. Mata Ramírez is Bachelor of Science in Physics from the University from Guadalajara, Master of Science in physics of the solid state and PhD in Crystallography the University of Barcelona, ​​Spain. Is member of the National System of Researchers. from Mexico and has the PRODEP profile, recognition that endorses its consolidated career in scientific research high level. His postdoctoral training It comprises three stays in institutions of excellence. He Optics Department of the CIS 2002, the Department of Crystallography of the University of Barcelona 2003 and the Center for Condensed Matter Sciences of UMAN 2004-2005. Their main areas of expertise They are materials physics, the nanotechnology and the solid state with emphasis on design, creation and material analysis nanostructured crystalline, ferroelectrics and semiconductors. Since 2011 He works as a research professor. Well, his postdoctoral training It comprises three stays in institutions of excellence, the CS Optics Department 2002, the crystallography department of the University of Barcelona 2003 and the Center of Condensed Matter Sciences UNAN 2004-2005. Their main areas of expertise They are materials physics, the nanotechnology and the solid state with emphasis on design, creation and analysis of crystalline materials, nanostructured, ferroelectrics and semiconductors. From In 2011 he worked as a professor Senior Researcher C (Full Time) comprehensive in the area of ​​nanotechnology in the Faculty of Engineering, Architecture and Design FIA of the Autonomous University of Baja California, campus in Senada. Its production The academic work comprises more than 40 articles. in indexed journals, eight books, 10 book chapters and numerous contributions to national congresses and international. We extend our cordial greetings. Welcome, and we invite you to share your conference, Dr. Jorge Octavio Mata Ramírez. He The space is yours, doctor. Thank you very much, Alexis. Let's see. Okay, that's it. Can you see me? perfect? Okay. Well, thank you all. Uh, thank you very much for the invitation. Good morning. Well, today I'm going to talk to you about This is an outreach talk, why? Why are bubbles always round? Basically, the idea of ​​this talk is, uh Let's say, to liken what the... nature with the phenomena that of We want to repeat this in some way. technological applications, seeking Above all, optimization, right? This optimization therefore consists of save energy. Somehow, huh Everything we do is in function of matter and energy, but the Technology is about optimizing and somehow This is how innovation works, right? Transcend. Okay. Well, my name is Jorge Mata. Well, they've already said something about me biography, this, I thank you. Whom If you look closely at the image, we can see two bubbles. They are not exactly both Round, right? But what is true that they have a certain circumference, They are spheres, they are spheres, they are spherical, They depend a lot on their training and what It is true, it is important to mention because they don't have corners. There are many phenomena associated with the a The bubbles, right? In nature, They all have a subtle charm. These particles, right? And somehow manner on a microscopic scale They behave in a certain way, on certain scales. Smaller ones behave differently with exotic and large-scale properties macroscopic, otherwise. Yeah. Oh, let's see what happened. Well, first, basically what What we do is make a movie with soap. We make an emulsion, it We add water, we put some soap on it. Soap is a surfactant or surfactant. What is it? It is a amphipathic substance that reduces the surface tension between two phases, like water and oil. It has a hydrophilic head, That is, sharp loves, tune to water and a hydrophobic tail, that is, which repels it, right? Allowing then emulsification. Detergents are used for cleaning and in the lungs in our body for Cleaning, say, alveoli, facilitates breathing and somehow we It keeps you alive, right? The question The question that arises is, why are there no bubbles? pyramidal or cubic in the air or in the nature? Yes, the mountains are from Some pyramidal shapes, right? But the leaves have a certain circumference, No? They are two-dimensional figures, flat, but they also don't have corners, No? Then we can think of this universal geometry, right? Nature prefers patterns that are consistent, the tree trunks, the stems, They all have a certain symmetry. there is a A lot of geometry in it, isn't it? It is the Round shape, an aesthetic choice or is it an imposition of the laws of the physics. Well, the answer is actually Quick, isn't it? We always look for the principle, the principle of minimum action, of minimal energy, of simplicity, of plainness and within This simplicity, because there is a Complexity, isn't it? The absence of pyramidal or cubic bubbles in the nature is not a complexity aesthetics, rather, is a consequence direct from laws or arguments Mathematicians and geometrists, right? There are at least three reasons fundamental. The first is the area principle minimal, right? We tend to Optimize, right? Nature always seek the state of minimum energy. In a bubble, the energy is contained on its surface, on the skin of soap, right? Yes. That kind of layer that We see, yes, tension remains surface or surfactant, right? For spend the best amount of energy If possible, the bubble should stretch as much as possible. less possible and somehow remain stable. Yes. If we wanted to make a cubic bubble in a simple, because we couldn't do it, since we have a different geometry. In this case, the corners or vertices of the cube would be much further from the center of the faces. Let's remember this, shall we? For example, in a A triangle has three sides, right? A A square has four, a pentagon five and so on. If we We started incorporating layers, faces, faces, faces, faces, faces and we tended towards infinity, we would What we would have would be a sphere, TRUE? So, a definition of a circumference is a It is a polygon with infinite sides. So a sphere is a, let's say, it's a polygon with infinite faces, TRUE? If we could create a bubble square, the vertex would be much more farther than the one in the center than the faces, TRUE? And that would be an imbalance. energetic, right? This extra distance It obviously requires more tension, more soap films, which would mean different accumulated energy or more energy accumulated on the faces. The surface tension then acts as an elastic band that stretches the corners, pulls them towards the center and that disappear. So, look, it turn this into a sphere. To recap, a sphere is because It contains the minimum area. Yes. Two, the uniformity of the pressure. Inside a bubble, the trapped air pushes with the same force in all the directions. In a cube, the pressure in a corner would be different from the pressure in the center of a face from the point from the point of view of the radius of curvature. Yeah It would be somewhat unstable. There would be, let's say, two phases, two situations, two forces working in the same place And that would somehow change this pressure. This would create an imbalance mechanic. Surface tension would crush the tips of the pyramid or the cube because there isn't enough pressure localized air only in the corners to have this, let's say, sharp shape. And the third is the instability of these edges. For there to be one cubic bubble would have to would have to to have corners, these edges, the union of the two sides. These lines in physics we can We manufacture, right? They are movies thin, ultra-thin. An edge is a So it's a high-voltage zone and great fragility. Look closely here. Okay, later on I'm going to talk about drops, right? The water molecules on an edge are forced into things that aren't exactly uniforms, they are unequal, what causes the film to almost break instantly or curve inwards. So, the next question is, Can all these forms be forced? geometric? Yes, but with outside help. We can do certain tricks and We can indeed achieve this square bubbles, but we are putting energy into the system, we are creating another geometry, right? By For example, if we submerge a structure of cube-shaped wire in a solution of soap, I'm already putting the structure, let's say, square or cubic, Yeah? I already have the corners. Is So what I do is simply movies, flat movies in each one of the six faces of the cube, right? Yeah. We will see that the sheets connect towards the center of the frame. When blowing air right in the center we can create a temporary cubic bubble. Without However, at the moment when the bubble It comes out of the wire frame and is free. in the air, the tension forces superficial, let's say, uh, they act, Yeah? and in a very short time it either breaks or it breaks bubble or buy one again spherical structure. Yes, we're going to look at the principle of minimum. energy, right? In science, right? Language, In mathematics, systems tend to search for the melon energy state. For the soap bubble, the energy potential is stored in your surface due to this tension superficial that we will call From now on, range, right? The We define surface energy as range by area, right? So, energy It is equal to this range, this voltage surface area. Yeah? So that To minimize energy, the area must be be the minimum possible for a determined volume of trapped air. If you look closely, in many of the bubbles they are not exactly perfect, they depend a lot on geometry. What is certain is that It has a radius of curvature, that is, They have no corners. Here I can see perfectly a structure, well, it's hypothetical, It is a structure, If you look closely, they are hexagons. that somehow They enclose something and form a structure spherical. Yeah, In nature there are links such as those of carbon, those of boron, which we allow building this type of structures. Yes, these structures have many applications in catalysis, in nanotechnology that we will see later. The isoperimetric problem, isn't it? Mathematically the question is, given a a fixed amount of volume, what is the geometric shape that minimizes this area superficial? Here I have an image where I have, let's say, a sphere and it's embedded inside a cube, right? He The cube has an area of ​​because its side length is times its height. Side by side, right? And the sphere, Well, I know it's 4/3 of pi times the radius. cube, right? Then I'll see which one has it larger volume, right? Obviously it's more The larger the cube, the greater its volume. It has a larger surface area on its faces, But what is surface tension like? No? If we compare this cube and the sphere that contains the same volume for a Given a given volume, then I have to Volume is side cubed, which is the root cube of b, right? Then I get a The value is six, right? for a sphere of radius R, because I have exactly this and I see that The volume is 4.84, right? If it is younger, right? In conclusion, look, the sphere uses approximately 19% less surface area in a cube for contain the same air. The nature of This way, let's say, optimizes, right?, the material from its surface to make This skin and obviously what forms It is a sphere. Yeah. There's another equation, well, it's the law of la plas y jong. The round shape too It is explained by the difference in pressure between the inner skin of the bubble and outer skin. Yes, the equation of the spherical plus jongficie two-layered like a soap bubble This is it, right? Where delta P is the pressure difference. Gamma, like We had seen, it's the tension superficial. Yes, this is the one Applian that multiplies strength normal. Yes, I forgot to put it here. This, right? Yes, HF is the average curvature And N is the normal to the surface, No? So that the bubble is in mechanical equilibrium, internal pressure It must be uniform at all points. If the pressure is constant and the tension The surface is uniform, the radius of The curvature must be constant throughout the surface. The only figure closed geometric shape with a radius constant curvature at all points, It's obviously a sphere. Yeah? So We can say that the bubble is round. because mathematically the sphere is the solution to the optimization problem of minimum area for a fixed volume and physically because it's the only way that allows surface tension and the internal pressure reach equilibrium perfect and stable. So, let's go this way. What is exactly a bubble? Well, it's the path of least resistance material. Yes, nature in this sense is efficient, is optimal, is not always seeks the mendron state of possible energy. The sphere is the shape geometric that allows enclosing a volume given with the smallest surface area possible. In the case of a surfactant With the soap, look, we have A movie, right? It's a that he we call it thin film. This movie Well, it has a certain thickness that depends From the surfactant, right? If we If we force the bubble, we can do it. bigger. If we could blow, I could to become bigger and bigger. Can even putting bubbles inside one bubble. Yes. So the skin, let's say, This surface can be stretched. It is obviously maintained by tension, but it can break. Yes. So, one A bubble is a thin layer of water soapy that encloses air, encloses a gas. So, it's a difference of two. fluids. It's a layer inside, well It has a gas. Then the soap reduces the surface tension of water. This The bubble has two surfaces, the face from outside air and the water air face the interior. Each one tries to contract the minimum possible and the two coexist. They coexist in the bubble, in a system of balance. So, the bubble adopts the form that maintains the balance between the internal pressure of air and the tension of the film with the abroad. Yes. I have a small one here. Image showing the bubbles that... They somehow clump together. Yes. And well We see colors. Now let's see what they are exactly the colors, but first, Well, These bubbles are usually made of a small amount of oil, yes? and water, No? We know that molecules Water molecules are polar; they have one side positive, they have a positive charge, It has a negative charge. Normally the positive charge because it is the metal and the negative because it is the contrayón, in this oxygen is one such example. And they attract each other electrostatically, yes? As if they were animals, right? And these are called forces of cohesion. We can make this molecule water molecules bond with each other and to another and another and another and so that one is formed something called a drop. A drop is full of many water molecules, TRUE? But it's an interesting thing. water because when we If we start throwing, Let's say, small water molecules on a surface in a, let's say, uniform way, We see that drops are forming. I don't know if you can see my mouse, but look, because For example, there are large drops here, there are smaller drops, but what is The truth is that there are areas where there are no There's water, right? Water tends to attract the molecule, to stick together and somehow form These islands, these small islands. Are The islands are thus maintained by the tension Superficial, isn't it? Surface tension on a surface the molecules, let's say They do not have here on this surface the There are only water molecules below. Above There's another fluid, isn't there? Which is in This case is air, right? Yes. No. to have molecules on top, a small layer is created in the surface. Yeah. They bond electrostatically more strong at the sides and downwards and then that little one is created layer that is the surface tension that somehow maintains a tension. Yeah? It is what allows some insects walk on water without sink. Yes. Or what we call in Mexico was the straw that broke the camel's back, wasn't it? A small layer is created that maintains joined to the drops, to the water. Yes. And stores energy. Yes. It's durable. Is resistant. It has many properties and above all these properties They multiply at nanometric scales, right? We'll see about that later. Yes. Why do we need soap? unfactant. Pure water cannot To sustain a bubble for a long time, it It breaks due to its own tension. The molecules, in this case, of soap, are interspersed between the water molecules, reducing This tension and giving it that elasticity. Here we can clearly see that Bubbles are round, right? And we can also see that they stick together, TRUE? They are linked. Yeah, There are forms, let's say, of wire that can we this manipulate so that the bubbles are as if they were small cylinders, but If you look closely, all the bubbles have radii of curvature, right? The soap then creates a kind of let's say We call it in a heterocture, a sandwich, a layer of water protected by two layers of soap molecules, TRUE? The sphere and the area were minimal. Yeah, Look, a cube, a cube obviously already we had seen in general terms, then It has six faces, right? Yes. And the A sphere has the smallest possible area. Yeah. Less area means you need less energy to maintain the structure united. Yes, there are many problems. mathematicians. For example, there is the squaring of the circle, right? Relate this. Us We're talking about volume and we know that the volume of a sphere is smaller energy. Yes, for the same conditions, let's say, of distances between cube and sphere. Yes. Internal air pressure. Notice the air trapped between the bubble pushes outwards. The tension superficial pull inwards. So It's a balance of power, isn't it? Second law, right? Well, laws of Newton, right? Yes. The force equals mass times acceleration, right? In this case, then I can consider that the force internal is balanced by force External, right? Yes. For each action. It corresponds to the action, etc., right? The sphere is the only shape where the The pressure is exactly the same in all the points on the surface, in all possible forms, cubic, pyramidal, irregular geometries, etc. A sphere is the one with the smallest amount of the outdoor area. Yeah? Well, all this What do we usually come here for? We copy the mechanisms of nature and we apply them in the construction of technology, materials, of optimization. Yeah, Look, this is what I was telling you. Wire frame experiment. That What happens if we submerge a frame of Square wire in soap? Yes, it forms a flat film, not a bubble. Look at the movies. Here's what I What I'm doing is using this framework that I do, right? square this face, what I I have the movie here, right? The tension is maintained within From the area side by side, right? I do it in six. I can submerge This cube inside one of inside one soapy solution and when I take it out there a film in each of the faces of the cube. I can blow and make it form Here's a kind of inverted pyramid. Inside, right? Obviously this one does It has corners, but the point here is that is supported by the structure or The cube frame, right? If I took out This bubble inside the air, what I I would see that it either breaks quickly or it It forms a sphere, right? If I use a, let's say, a square frame and the Bubbles will form when you blow on them. They will be formed bubbles, but these bubbles will have these spherical surfaces, let's say, curved surfaces. Yes. The movie. always try to stretch as little as possible possible between the edges. The bubble It's only round because it has no edges. that they limit it, right? In the That's just how nature is. We don't have square sheet structures triangular, we always have as curved shapes. Okay, let's look now at the law of the place, right? Look, the pressure change says that is equal to four times the tension surface between the radius. The The pressure difference depends on the surface tension and radius. The Smaller bubbles have a pressure internal rate much higher than the large ones. That's why we bubbles We can, let's say, embed small ones in. with a larger bubble and make it Get this gas inside, right? AND obviously this larger bubble It gets a little bigger until the surface tension on its surface no support and then it breaks, right? Yeah. Inverse relationship. How can we see in The formula, pressure is inversely proportional to the radius. If the radio decreases, pressure increases drastically. Yes, surface tension. In this bubble, the liquid tries to somehow make it smaller, shrink to minimize its area superficial. In a small bubble the The curvature is much more pronounced. is more pronounced, which requires a greater internal pressure to prevent the surface tension collapses it due to complete. The coalescence effect, isn't it? That's why Likewise, if we join a small bubble with a grante through a tube, a straw, a straw, I don't know, the little one It will deflate inside the big one. The oldest The pressure from the small one pushes the air towards where there is less pressure, which is the elderly. Here I have some photos where you can see They see very small bubbles that somehow They are always covering or trying to embed itself inside the elderly. Yes. When the bubbles come together, this... It's called bicephaly. If two bubbles of They are the same size, they join together, it doesn't work in a large sphere immediately. They share a flat wall, they share this wall, They stick together, right? The reason is that one shared wall uses material that two separate walls. So, this is energy savings. I can do this somehow implement in the thin films that I manufacture, in the devices, etcetera, right? For example, There's something called points. quantum, right? What they do is to form islands, let's say, they are deposited metals on a surface, form the islands and the islands sometimes are, Let's say, they're linked in this way, right? depending on the material to be deposited, No? So it's an energy saver that we can copy, implement, right? Look, in 1887, Well, looking for the let's say the minimum area in two dimensions, in the area, yes? What is the geometric shape? to arrange it in such a way that it is Perfect, right? In 1887 the question arose of how it could partition the cell space of equal volume with the smallest area of contact and the solution were the hexagons copied from honeycombs Bee, right? Yeah. solution of hexagons for two dimensions, right? The Kelvin Problem Kelvin proposed it for three dimensions and conjectured that the solution It would be a honeycomb of truncated eighths, But he didn't prove it; it was simply a a conjecture that was proven because almost a century later, right? In 1993, On the other hand, Wean, two physicists from Trining College in Dublin, they discovered using computer simulations, No? In foam molecules, a structure which improved the panel's performance, 30% by 3%. Theoretically, it was thought that Kelvin already I had found the solution. Yeah, This Wper Pearl structure is It is considered the best solution; it is the most efficient for the Kelvin problem, but it remains a conjecture that It has not yet been proven mathematically. Yes, this structure uses two types of equal cells volume. A pentagonal cedar do irregular, which means that not all The faces are the same. and a tetracycline 14-sided with two hexagons and 12 pentagons with slightly rounded faces curved. Here we can see the irregularity of the faces of These polygons, right? So, the assemble these polygons Reduces area, increases volume And somehow it's copied nature and we can implement it in technology. Yes, the problem isoperimetric, right? Well, mathematical question behind the bubble, No? What geometric shape encloses greater volume with minimum surface area possible? Well, we already saw the cube. six sides to one, the cylinder is, here I was wrong, it's 484 to 1, but the sphere That's the minimum, right? relationship surface and volume. The youngest is the most efficient and the most efficient is the sphere, right? Follow the cylinder and then the cube. The mathematical formula, If the surface area, the area is 4pi per squared radius. The area, the volume is 4/3 of pi* radi cuo. Us We measure volume in cubic units, In liters, right? Yeah. inequality isoperimetric, right? 36 pi multiplied by the smaller of the square is greater than or equal to than the cubic area. Equality is It complies. This equality only yes, only yes. The figure is a sphere. No other This geometric shape achieves this limit. Yeah? So, look, It's interesting to see how we can, Let's say, understanding nature and about everything amazes us. Okay, let's go now and look at the rules of Plato, right? Josepon, a Belgian physicist, discovered in the 19th century that in the foams the sheets soap is always found grouped together in 3x3 shapes. Yeah? And the angle of encounter, well, they are 120 gr. It is the most stable configuration in nature. The laws or rules of Palatú describe the structure and the geometry of these soap bubbles and of the foams, establishing that the soap films form surfaces smooth and uninterrupted. These are found at three angles. Obviously the angles are 363, they are 120º and join in groups of four. vertices with tetrahedral angles of 109.47º. Yes, look, this is very similar to the that hydrogen bonds with the oxygen in a water molecule, TRUE? So, these edges that are Come here, if you look closely, these are them 120º. If we can make art with We can't even do this. technology, making metallic foams, let's say make structures architectural and we optimize the tension in the in the In the unions, right? Okay. This webant structure, which It is the most efficient structure for organize bubbles in a space three-dimensional? Well, this is a geometric structure complex of polyhedra that of some They reduce and minimize this tension. Yes, this proposal exceeded expectations. from Kelvin that stays perfect from 1887. This structure of Wpelland is a complex three-dimensional structure. In computer simulations of foam. This structure was the best solution to problem. I don't know if you remember about the The Olympics in China, right? That they built architectural structures emulating this type of structure, These polyhedra, right? Look, here it is You can see some photos of what it looks like. construction. bubbles in space. Okay, now Let's watch something else, shall we? Look, in The Earth, well, gravity then It tends to, let's say, pull everything towards Towards the center, right? But in the space, because gravity works different way. Yeah, gravity slightly deforms the bubbles, it crushes them on the ground, but in, let's say, in space, what we have seen in space stations It's because bubbles are more like spheres perfect and can last much longer time. In physics, all the, let's say, Gravity is a force that relates masses to distance, TRUE? and masses, we're talking about the sun, planets, lumas, etc., right? Are masses, In other words, zero gravity does not exist. There is always a force that somehow The shape pulls on some object, right? Yeah. Definition of environment often called weightlessness or zero gravity. The term technically it's microgravity because very small forces persist. This is experienced, for example, this uh let's say microgravity at the station International space, right? He behavior that occurs in liquids, Liquids don't behave like that then Just like on Earth, they form bubbles and the The materials do not settle, which is vital for fluid dynamics research. I'll see if I can run this video. TO Look, here we're going to see how in the These space stations are formed bubbles. Yes. And how can you drink them, right? Look. Yeah. But if you look closely, the surface is curved, right? Look, here I go go back. Well, I don't know if I can go back a little. Let's see. Yes. Let's see. Look, this bubble is completely spherical, right? But look, when It is coming out because of the movement it forms a kind of ellipse. And in the last one, let's see if it shows up. Look, do you see? It's a little long, No? It starts to spin, rotate, rotate, rotate, broken and well, it ends up becoming A sphere, right? Okay. Let's see. Okay, now let's move on to see Biomimetic architecture, right? The the Ping's water bucket, right? Its structure It is based on the geometry of bubbles, Yeah? Maximum structural strength with the minimum of steel and material. Interestingly, this is it, look, it's the optimization, which is what of what We're talking, right? How to copy the bubble structure we can some way to design structures that somehow optimize materials, spaces. Yeah, I was telling you about the bee plan, right? Bees use hexagonal cells to divide a 2D plane in a efficient. Yeah? So, look, this shows that the The hexagonal shape is the optimal shape in 2D, yes? But in 3D, well, I had already seen them commented that it was the one at 12:14, TRUE? The irregular ones, too. Okay. Well, depending on the thickness of the film, some color waves They cancel. Why do bubbles have colors? TRUE? What's going on in its surface? Because? Why are some seen more? I didn't put yellow ones here, but there are some that look yellow, red, etc. Well, that depends on the thickness. We'll see. colors like blue and green. The Gravity usually pulls the liquid towards down, so the base of the bubble It is usually thicker and shows these tones. the smaller thicknesses. Tailored that the water or liquid evaporates or It drains, the colors turn to yellow, Then let's say magenta, to reddish, right? So, in a way, it's about starting with the blue, green, yellow, yes, orange, etcetera, right? Newton's black man, that's what he's called This is when you see a dark color in the The bubble is because it's about to To burst, right? The sign of the end. Fair before, let's say, the bubble bursts, the top of the bubble It comes back so thin, less than a tenth part of the length of light, which all visible waves are canceled by destructive interference. Yeah? Then, an area with an absence of is seen. black light. Yeah? So if we see a black spot in the expanding bubble at the top of the bubble, this This means the bubble is about to burst. collapse. Yes. And it's about to break. Yeah. This color is therefore due to the interference, the interference of a thin film. Light waves bounce off the inner and outer layers of the bubble. Let's remember that a bubble It has two layers, the inner and the outer. External, right? Yes, the color tells us how thin it is. the bubble before it bursts. Look, Here we can see this color of rainbows and we can see these little ones black zones that somehow us denote a greater thickness on the surface slim. Yes, here we can see what they I was talking about the 120g angle and how how the bubbles join together and how they stick to the walls, optimizing, let's say, the wall, right? The tension. Okay, so what apps do we have? No, We, for example, can coat certain molecules, This is nanotechnology. We can deposit a few, huh? molecules, no longer use so many for to attack a certain problem or solve or above all, optimize, reduce size, reduce materials. Yes. In biology, because For example, the alveoli of our The lungs function in a similar way, Yeah? They need surfactants, because in In this case, they are lipids and proteins, right? To avoid collapsing from the stress superficial, without functional bubbles in We wouldn't be able to breathe with our lungs. So, so, basically, what Are they gas? This surfactant that there is Here in the lungs it's a mixture complex of lipids, fats and proteins produced by cells called type 2 pneumocytes that are produced here in the alveoli and what they do is some way to emulate this. The gas arrives somehow, this is a surfactant and somehow protects, allows a certain step, etc. Yeah, we breathe in technology. Well, for for spacecraft, for let's say structural supports, yes? Prosthesis, Our bones, if you look closely, are composed of three types of cells, No? It's a kind of spongy fabric, one They are striated, right? And one is smooth, right? the part exterior, but the interior part... bone is resistant, it has a structure of this type and we of We somehow copied it to use it for the space industry, metalworking industry, etc. Are They're light because they're mostly air, right? They're foams, they're solid foams, right? Structurally they are strong thanks to the geometry that we copy from the bubbles. These are just a few examples, but This is not as simple as it seems, No It is truly a copy of nature. Nature knows how to optimize. Yes. One Metallic foam is a porous material and light. It is generally composed of aluminum nickel containing bubbles of a gas that may be sealed or interconnected. Yes. It combines rigidity, low density, absorption of energy and fire resistance. It what are you doing which makes it ideal for applications in automotive, aerospace engineering, construction, civil engineering, Let's say, architecture, shielding, according to its main characteristics. Look which ones. High porosity, generally exceeds 95% cell voids open. It is light, much less dense a solid material, ideal for reduce weight in structures. There are often mixtures of ceramics, of polymer-based cements that have sometimes material, let's say, air encapsulated, as on the rock, in the famous franging that what we have is oil stuck in the rock, gas trapped in the rock and of We'll replace it somehow, right? We copied that. Energy absorption Excellent for impact and cushioning. thermal and acoustic properties. It's a It's a good thermal insulator and it's a good sound insulation. Types of materials, closed cell, the pores are sealed, ideal for buoyancy and high structural rigidity. Open ones have pores interconnected used for filters or as a support for catalysts, for gases, for the engines, right? Commoner They are made of aluminum, but We can also make alloys or mix with nickel, steel, copper, tin, etcetera, right? In catalytic converters, well, normally We don't use palladium, rhodium, or platinum. I know, expensive materials, more applications Featured, not for engineering aerospace, sandwich panels for lighten and strengthen the wings, trains of landing, armor on vehicles of luxury. Somehow, how is it... calls?, the deformation of these materials absorbs energy and can serve as support, right? For construction. Can use them as sound insulation, bridges, structural elements lightweight, durable. In the industry, high-efficiency filters temperature, heat exchangers and catalyst supports. In electronics, We use them for batteries. The The batteries are gel batteries. It is usually a gel that has metallic ones there. The Covering nquil foams are used as electrode and shielding material electromagnetic. Well, This is efficiency, isn't it? Here we have an example of surface tension, a leaf as it floats. If you look closely, you'll also see the The leaf has curved surfaces, TRUE? There is a corner here, but Well, it's supported by the stem of the leaf, right? Here we see how it is, how it is These bubbles assemble, don't they? It's a minimum area, there is a contraction, there is a maximum energy savings. So, we can conclude that this form circular or this round shape is a optimal mathematical organization, right? Yeah. Here we can see the bursting of a bubble. how to fragments into smaller bubbles Small, aren't they? Something so tenuous, so ephemeral as a bubble, physics describes these laws that somehow uh because they behave in nature and last for always and I can somehow implement in the study of other things, right? No I know, on a surface, how particles move, etc. light, how it interacts with the surface, how new ones are created particles. Yes. Well, this is the law. It was a review of the law of PL Jong, We had already seen that it is twice. Notice, the factor four appears because Both, the bubble has two movies, an interior film and a film abroad. Each one contributes to this Form 2 range between the radius, right? The Smaller bubbles have a higher concentration of bubbles. internal pressure, that's why when two are joined bubbles of different sizes, the a small bubble, let's say, deposits the gas in the larger one, right? In balance, the internal pressure holds exactly the extent of the surface, that's why the optimal or resulting form is a sphere. Yes, when geometry becomes art, No? Notice, on a minimal surface is that whose area is locally smaller possible, giving a fixed outline. His mean curvature is zero. At each point The catenoid is not present. minimum area The revolution appears when you join two rings in a soap film. Well, This is the figure I found. So. Unicode is a surface in spiral like a screw, right? Locally flat with average curvature moon, null average, infinite and without self-interference, right? It's a screw, it's a torque. And the plane, then, is the surface. simplest minimum of two dimensions, zero curvature everywhere. If it is an example, but it's about conveying the idea. Yes, there is one thing that mathematics we call it calculus of variations. The math tool mathematics, well, this is the language, No? An ordinary calculation finds a minimum of a functional function of areas. Define mathematical expression that measures the area of ​​any surface that Enclose the given volume, right? He variation calculation is found a function in a form that neither minimizes a given amount, right? There is the equation of Ho la grang que aplica condición de minimum. The derivative of the functional must Therefore, it is zero, and so it gives us a differential equation that can write the system, right? The only one a solution that satisfies this equation with mid-curvature and the sphere closes a fixed volume. Well, in nature the sphere It appears everywhere where energy It's important. Yes, on planets and Stars, yes? The planets then They are spherical, right? The stars They're round too, aren't they? Gravity It acts in all directions with equal force force. The result is somehow a sphere. The Earth, the Sun, the Moon They are almost spherical. Well, we know that The Earth has flattened poles, No? But the general idea is that it is by gravity. Well, it has the same radius, right? The raindrops, well, in the void the The drops are perfectly spherical, in The fall deforms them in the air, but the surface tension, let's say the It remains stable in some way. In biological issues, cells and vesicles, the spherical cells They minimize their membrane. Yes, the vesicles Lipids are perfect spheres, aren't they? In the great iso, for example, formed by the accumulation of layers of water frozen, its spherical symmetry minimizes the interface of the surrounding air. The gas planets Jupiter and Saturn are They are flattened, but the tendency is to Being spherical dominates thanks to pressure gravitational. Yes. And finally, well, the nanoparticles. In nanotechnology, the Spherical particles are more stable because they minimize the surface area ratio volume. We, well, we do a things called quantum dots, No? We make deposits in large structures. When we make the deposits, many Sometimes these islands that form pass information or electrons pass from one Drop by drop, and they emulate as if it were a atom species. What applications do we have? Well, then In architecture, specifically for construction, Yes, they have an aesthetic and above all they are They optimize weight, structure, and They are distributed in a regular manner. In In medicine, microbubbles are used as contrast agents in ultrasound and for transporting medicine directly to the affected areas or diseased areas, right? In physics of materials, the metal sponges and The ceramics are inspired by bubble structures and offer high resistance with very low weight, resistant to the pressure. When a bubble forms getting smaller and smaller, it becomes more resistant and has almost as if it were a solid, right? In computing, well, the algorithms of minimum surfaces apply in 3D graphics meshing geometries complex and above all, let's say, help us improve the design that We do it by computer, right? Okay, here's a little story Of the spheres, right? Since the year 200 BC, if it was increased again formally that the circle has the larger area. Yes, Oiler worked a lot on the calculus of variations to find optimize this. Charz demonstrated that the sphere minimizes area between closed surfaces that enclose a fixed volume. Horwitz tested a test using Fourier series. The Fourier series, well, normally They relate sines and cosines. Yeah. generating this a description of the The geometry we have, right? Hching demonstrates the bubble alterer using differential geometry advanced and so on. No, I didn't add any more. Yes. Finally, well, this is a... So it's like science fiction, isn't it? Is the Dyson sphere. The Dyson Sphere It is a theoretical megastructure that surrounds completely a star, one, I don't know, a star, because a star is... energy that is going out and That's the way to optimize it, isn't it? Is science fiction, it's not to capture the most of the radiant energy proposed by physicist Freeman Dyson in 1960, designed for advanced civilizations with extreme energy needs. HE considers it more viable as a swarm of satellites, solar panels that, like a solid shell. It is searched for using the infrared radiation detection excessive. What does that mean? That we in the universe can look for areas where there is a high density of infrared radiation and we can see how let's say Bubbles can form in space. No, we haven't found them, but oh well. Theoretically, it's a good argument, and it is a simile. No? Okay. As conclusions, Yeah. The bubbles minimize their energy reducing the surface area. HE then you can see the beauty of the mathematics in every bubble. The sphere is the only way that contains the maximum volume with the minimum area. The form The spherical shape of the bubbles is not a not aesthetic coincidence, but a choice masterclass in energy efficiency. Thanks to surface tension, the Liquid molecules attract each other with such force that they seek to minimize the area of ​​contact with the exterior. Geometry then dictates that the The sphere is the only shape capable of to contain a certain volume using the smallest possible surface area. In this way, nature saves energy by reducing the voltage to a minimum. Therefore, we can conclude that a The bubble is the perfect balance between the internal air pressure and the hug contractive of physics. And from a technological perspective industrial, seeking applications, the Bubbles are a tool of fundamental precision. In mining They are used for foam flotation, to separate valuable minerals from the rock. separate amalgams, etc. He water treatment, the bubbles of air or ozone eliminate pollutants and They oxygenate ecosystems. In medicine We use vehicles for transport drugs. Yeah, There are some experiments, well, there are some Well, yes, let's say, there are some research in which we use bacteria that have shapes, well circular like bubbles, the We pollute with particulate matter and the we can introduce it into the bloodstream and Take them to the affected areas, right? Yes. Releasing these medications in exact points, using ultrasound, We make them explode. Yes. Also, in the food and cosmetics industry controls the texture and stability of products. And finally, the bubbles They are key in med cleaning ultrasound, where the collapse generates high-energy microjets that They disinfect the surgical instruments and complex industrial parts. And well, that would be all. I don't know, thank you for your attention, and well Here we are. Let's see. I'm going to stop sharing. Okay, ready. Yes sir. Ready. Well, we thank Dr. Mata for your valuable intervention. Next We're opening a question and answer session. part of the auditorium. Well, in this We're currently connected on YouTube Dr. Mata Ramírez and there are some questions that I've been gathering from the chat YouTube. So we have a question from Elwar. Elwar says that if the bubbles They get excited, what happens between them now What are polar? Okay, let me see if I understand the question. If They excite, so what do you use to excite them? With electromagnetic waves? Conas mechanics, etc.? Normally a because the bubble tends to grow. Yeah. Hey, in the case of molecules of water, look, when you excite them under Under certain conditions, what can happen is that you manage to embed another metal. Yes. Instead of H2O you can make H3O. Yes, you can make molecules. I don't know if That's what you mean, right? With the with the disturbance. It is electromagnetic, it is Let's say it's a matter of temperature or whatever. If you increase the temperature, because you break the bond. Yeah, But you can couple atoms. Yeah, No, no, I can't hear you. Alexis, Okay, doctor. Thanks a lot. Okay, we have another question here in the Suleima's chat Rosemary, It says the following. How is it demonstrated that the Wferan structure has less average surface area that the Kelvin's original proposal? Uh, look, I don't have the exact answer for you. I can give because it was a simulation, No? Uh, when you do a simulation, Well, it's like taking a... The computer, right? I'll give you an example, shall I? I I remember once when we were trying to optimize in one area Two-dimensional spheres, right? So, we came to the conclusion that for that side by side, and those spheres could fit 33. Yes. And I remember that someone arrived and... She put them in different layers and He managed to score three more. Yeah, He managed to score three more, let's say, when we placed them as we did random, Well, let's say there were, I don't know, 43. Yes. And when this person started to arrange them then He managed to score 46, right? How did he do it? Well, somehow it optimized. We can simulate this on a computer, obviously with The structure, if you look closely, was 14 sides and 12 sides and that were not irregulars. We can simulate it and we can obtain. If you look closely, the The variation was 0.3%. It was more optimal, wasn't it? But this Mathematical proof is not yet available done mathematically. It is a simulation. Yes, it remains to be proven. Yeah, Okay, doctor. Yes. Well, they're already there. We currently have them active, uh to the participants in the chat YouTube. They are doing a variety of questions. I'm trying to take the most general questions So that you, as the speaker, can... clear up those doubts. Well, I have another one. John Brando's doctor asks a question Dominguez, almost identical to the one Zulima made Rosemary. How is it proven that the Werfel structure has a smaller area average surface area that the proposal Kelvin's original? Well, it's There is no formal proof, but in a simulation is demonstrated, Let's say, based on the program's outcome, No? You start giving values, right? AND You start to get answers. So, It is a It's a consequence of your programming. No? It is a consequence of the computer argument that you give it. Yes, but formality, if that's what you mean. You mean, well, there isn't one. There isn't one, that as far as I know. Okay, doctor. Well, a lot. thank you. Okay, let's continue here with the questions. We have one from Luis Fernando Montenegro. If gravity and wind affect the bubbles, why do they still tend to can it retain its round shape? Well, it's the principle of minimum. energy, right? And this superficial, uh, let's say It's like the It's like when we see that We're making a bonfire and it's exploding. Let's say, something that thunders, right? It What we see are small, let's say, incandescent points that rise into the air, They're on fire and suddenly they end up in ash, they are not consumed. In a bubble The thing is, we have to... surface tension It is due to two layers. That's that layer It has a certain thickness and it has a endurance. I don't know if you've noticed that There are bubbles that I think the record for the most bubbles The large ones are meters long and there are also bubbles where there are records where to the They put more bubbles in the bubble than I know what. How many have they put in, a hundred and something bubbles inside a large bubble, No? These bubbles last over time due to the thickness, due to the surfactant, No? But it's the combination of the surface tension between the layer inner and outer layer. Yeah. I don't know if it consists Yes sir. We continue with more questions, taking advantage of the space of time we have left and to all of us participants who are in the YouTube channel, this is the moment, eh It is relevant for them to do questions. We're going to general compilation. Okay, then I have José Alfredo Herrera Villamizar, Doctor, tell us where you think we are would end up leading this investigation. Do you think there are still more things to come? discover? Interesting question, doctor. Uh, yes, definitely yes. we h because far from the pleasure of investigating to investigate, we always seek uh, let's say, adapt this type of research into optimization, by example, uh the link of items. For example, a while ago they He was talking about fracking, wasn't he? Us We have heard about fracking from oil. What does that consist of? really? No? If you look closely, I'll definitely see it. of oil that somehow this or We already extracted the oil and they remained only remains. So it's drilling, Yeah? To expel water or sand and detach the oil that stayed there or the gas from there and take it out. It's about replacing. How are you Is that oil trapped? well it is trapped in porous surfaces, type bubbles, right? So studying them will help us It helps to obtain resources and energy. She The last slide was this sphere of Dyson, right? He is a figure of science fiction, but in the end it is a sphere that Inside there's a sun, it captures energy because we're supposed to use more and more energy. What's next? well, somehow discover What other surprises does the nature and adapting them to technology, incorporate it into the design of materials. For example, carbon fibers are They are lightweight, they are durable, they are expensive. But they help us a lot. Can emulate this and make materials orthopedic, Yeah? simulate bones that are lightweight, resistant, biocompatible, etcetera, right? Neural networks, right? Now that we're on the topic of intelligence artificial, we can emulate these bubbles for that help us in calculations of operations, optimization, etc., drugs, uh, I don't know, tissue regeneration, etc. There's a lot to do in There's a lot of technology. For example, on cell phones, in nanotechnology, What we do is that in the same We have more applications, more space functions, etc. And that's due to accommodation. To the accommodation. The arrangement isn't exactly geometric, it's not about squares, pentagons, yes, it is often emulating bubbles and making technology with it. Yeah, ready. Yes sir. Okay, so here We continue. Okay, they ask us a question Interesting, doctor, regarding the airplane windows. They tell us that if everything that has happened to us spoken has to do with, eh, that the airplane windows not be square, but ending in circles of subvertices. Yes, it is related, but Hey Yes, let's say, a way, a way, a form of minimum energy, since they are the curved surfaces, yes? within the airplane windows, because the plastic or the material it is made of, Let's say, the material is transduced, I don't know exactly If it's a square plate and the thing about Is the outline round or if it is round? No I understand that it is, and I understand that it is a way to make the resistance more efficient air pressure because there are two pressures, internal pressure and the external pressure, right? But if It would make sense, it would make sense, wouldn't it? make them square because the pressure is maintained more, let's say, balanced if it had a curved surface. Ready. Yes sir. Very good. Well, So I have Hugo Ruano because it is evident in the universe that Everything tends to be circular and take from spherical shape. Is that right, or is he mistaken? Says, No, yes, this is, for example, ours The skull is, let's say, spherical. No? Yes. Somehow, the bones, then. They are cylindrical, but they have a circle, No? Well, there are topological theories which tell us that, for example, the The universe is a donut, it's a bull, isn't it? AND A bull is nothing more than a A circle made of circles, isn't it? Yes. Many leaves are round. Yeah, Our legs are round, let's say, in the sense that they are cylindrical. Yes, nature is efficient at that. sense. It is efficient. And I think the universe tends to be like that. Because, well, the universe is expanding. We don't know if it expands upwards or downwards, but it expands, right? Yeah. Stars and planets are Round, aren't they? The circle is part of us. Our eyes are round, They are spherical. Yes, etc. So, yes, there is one. trend towards circularity in the nature rather than the angles towards the curves, I would say. Well, that's what you're telling us, doctor, Everything around us has a shape Geometric, isn't it? Yeah. Nature has geometric forms and because we need to take advantage of the geometry of nature. Well, here's a Interesting question. doctor, what does JTM do? 486. He says, "In what way does intelligence artificial intelligence and quantum computing have helped nanotechnology?" Hey, For example, uh, a lot, a lot, a lot, a lot. Before, for example, in, let's say, the Nanotechnology is now an application From physics, right? It used to be very difficult to manufacture From nanoparticles to nanomaterials, right? It's much easier now, but 20 years ago years ago it wasn't. It was difficult. So, there used to be a division between what was, let's say, theoretical physics and experimental physics. In fact, there had been a Um, let's say a certain rejection, right? The Theorists, therefore, protested against those of the Let's say of the experimental ones, but there were a very important kind of conjunction which was called, let's say, physics computational or simulation. So now the computational physicists simulated materials that the theorists and the the experimental ones were manufactured. But of soon the experimentalists found new things or computational They proposed new things that later Theorists had to somehow formalize. Now, with the advent of the computers and intelligence artificial, we can propose new materials, optimize as This simulation of optimizing the area and The volume of 3D figures, right? Yeah, It has a lot to do with it, a lot. There is a material that is made of pure carbon, which is a single layer called graphene, right? Okay, we can propose which element it is similar to carbon that can bond And there is the borophene, the phosphorene, which are materials that They were already manufactured in some form laboratory, they have already been simulated and already They theorized, didn't they? They are theorized. So, Artificial intelligence has helped a lot in nanotechnology. Nanotechnology is nothing more that its application at nano scales by 10 to the menu9. It's engineering molecules, it's atom engineering. TO We can incorporate atoms into molecules different, change properties. By the by incorporating another cation, it we can make it transparent, flexible, magnetic, etc. We can do that To simulate, we can think about it with AI and We can manufacture it in the laboratory, We can theorize with AI, and so on. AI It's something that's here to stay and which has helped us a lot. We will surely move forward much in technology thanks to AI. Ready. Yes sir. Well, nowadays We are in the age of intelligence artificial intelligence artificial was created to support the processes, right? Scientists, educators. So, we have to make the most of it. Well, I have John Cano who tells us that bubbles seek the minimum surface energy. What happens at the molecular level in the point of contact where two bubbles meet They merge so that the interface goes from From being curved to being completely flat? What's happening? Well, it's optimized energy. Let's say each of them It's a tension, isn't it? She is tense. When that part sticks, let's say, it leaves Instead of being tense, it becomes like a kind of of flat film and the balance forces, it does not hold. In fact, I could tell you that those two bubbles that stuck together tend to live longer. Yes, they are optimized. they will last longer the internal and external pressures and They will maintain. The same applies to three, four. I don't know if you've seen, for example, when it's soap foam that makes A lot of foam, when it's a lot of foam It takes a while to dissolve, doesn't it? HE distributes the energy between them and from They persist in some form. Yeah, ready. Well, yes, sir. Ready. Hey, Doctor, thank you very much. No, uh, one last quick check. Okay, here's one last question. I know that, uh, uh, your talk has been so It's interesting that here in the chat we have quite a few questions. Give me a second that slipped my mind. Well, here's another one I've got ready for to conclude this question session and to conclude this presentation. Okay, so how do you demonstrates that the structure of W Plan has a larger average surface area that the proposal originally by Kelvin? Yes, I already knew her. What's her name? It already comes ready-made, but really this I'm thinking about how to give an answer different, but It is demonstrated by simulations, not It demonstrates that no one has done a A formal demonstration was indeed made. simulation and found an optimum older, right? To make a mathematical proof, What we need is, let's say, extrapolate it and do it for n of some form it in mathematical language Formalizing, right? I think that There is no proof. I believe there is a simulation and that simulation gives that result, but the mathematical formalism It's not like that. Yes, as far as I know. Yeah. Okay, doctor. Well, to all those who are at that moment connected to YouTube, remember that we are on an international conference entitled Why are bubbles always round? The secret of nature to save energy. We are accompanied by Dr. Jorge Octavio Mata from the University Autonomous University of Baja California, Mexico. Well, to finish up, doctor, I'm going to to give way to Dr. Daniel Steven Moral to Let's close this and continue with our basic science textbook. Dr. Daniel, the space is yours. Hi, Alexis. Thank you so much. Well I would like to give special thanks to Dr. Jorge Mata for having accepted our Invitation to our workshop basic sciences, uh, so this is the beginning of an academic relationship with the University of Baja California, Autonomous University of Baja California. Uh, thank you very much. I see, uh, well Here are several congratulations. Uh, le They comment, "I congratulate you, doctor, on your chat. Thank you for showing us the beauty of mathematics in the bubbles. I also find the subject, mathematics and physics present in nature and also Well, to encourage the students, right? Uh, many, many of these topics, uh, like I was just mentioning it. Professor Jorge, they are even that old as one might think. Uh, even from The ancient Greeks are coming studying the circle, the sphere, uh with plut with a little of the part of the trigonometry, the beginnings of trigonometry. So, uh, all this beauty of nature, because it is giving us as a reflection about that trigonometric study mathematician, which we often see trigonometric functions or we see the differential calculus, integral calculus like, uh, like those branches, very, very formal mathematically speaking, but because there is an intrinsic relationship with the nature, which is very important, eh never lose from A and besides that, well that now with these new generations that already have the part of artificial intelligence, we have the part of simulations, all of those observations that even, as Dr. Jorge was just mentioning that. that come from Gauss, from Oiler, eh They may be, well, even proven and mathematized by all these new technologies. So, uh, Dr. Jorge, Thanking you very much, and well, with that So we'll close this. conference. Thanks a lot. Thank you for the invitation and Well, we are here to serve you. Well, I want to finish by giving her the Thanks to Dr. Mata Ramírez. Very Everything you've shared with us has been enriching. this morning. Doctor, we hope to have again with their valuable presence in future events organized from the basic science chain of the School of Basic Sciences, Technology and Engineering at the National University Open to Distance Learning. Thanks a lot And we conclude the presentation. international titled Why do bubbles always Are they round? The secret of the nature to pray for energy. Thank you very much, Dr. Jorge Octavio Mata, for your great contribution on this day. It's day two, math day. In the morning session we are in the mathematics from the sixth workshop of the basic science chain. So, We conclude this wonderful presentation. Thank you. Thank you all, and well... day and go ahead with your workshop. Congratulations. Thank you very much, doctor. Well, So, uh, we invite everyone who They are connected in the YouTube channel. In a few minutes We will continue with our agenda. We're going to bring in a speaker national. So I hope you are Once connected, give us a few minutes. while we transition speakers to kick off our second presentation which is a national conference. Thanks a lot To everyone who is connected and following That's why we're bringing a very... Interesting for them to stay connected with us and let's continue enriching it which is all academic and all that investigative, which is sought from the basic science chain. Many Thank you all. In just a few minutes We will return. ia He He. Okay, let's continue with our agenda. We now proceed to the national conference. titled Connecting minds and codes, a journey to through the world of robotics and programming. I want to tell you that we accompanied by Master Lina María Toro Quintero of the Educational Institution Southern Citadel, Colombia. Lina Toro Quintero holds a master's degree in computer science applied to education in systems engineering with more than 14 years of teaching experience in information technology. Currently it is works as a teacher at the institution educational citadel of the South, where leads training processes in programming, software development and educational robotics. He is the leader of the institutional team of robotics and creator of the meeting of Ender robotics teams, initiative which has impacted hundreds of students in strengthening the Steam skills. has led training programs in thinking computing and girls' empowerment in science and technology, consolidating as a regional benchmark in education. Their teams have participated and excelled in settings such as Marlap, Firlego, National Lakaton. Her work has been recognized with multiple distinctions between it the medal for excellence in teaching and the Delvina López Order for Excellence educational institution of the city of Armenia in the year 2024. We extend our warmest greetings Welcome and an invitation to share her lecture, Dr. Lina María Toro Quintero. Welcome to this sixth science chain workshop basics. We met this morning on the mathematics day. Welcome, Dr. Lina. Thank you so much for the invitation. I'm very happy and excited to be there today here. Hey, Okay, they tell me When do we start, and right away? Yes, ma'am, the stage is yours now, now. You can start. Ready. Are you looking at my screen? Me Do they confirm? We are currently viewing your screen. Yes, ma'am. Ready. So I have it right there. Ready. I hadn't used it in a long time. AND They are watching my presentation of PowerPoint because I'm sharing my is in That? Ah, yes, PowerPoint wasn't in yet. presentation mode. Yes, I already put it. They count if they receive it. to be in this science workshop basics. Thank you very much for the invitation, especially since, uh, to Daniel. Okay, I'm going to tell you about my experience. from robotics clubs and the projects I have participated in and for Of course, we're going to talk a little bit about How have we had math? as I have called it for the day of Today, uh, invisible mathematics. So, welcome, and uh, that's it. a journey through experience that We have had through robotics and the programming. Uh, I log on and I'm representing today at the Ciudadela educational institution from the south of the city of Armenia And welcome to Connecting Minds and Codes. Well, perhaps some of you have I laughed at this meme that's here today. Uh, maybe we've felt this in different moments in our lives, TRUE? Another beautiful day without using the perfect square binomial or the perfect square trinomial or the root square. Uh, I've heard a lot I've seen jokes like these, and in At some point I have identified with they. In our role as students, on many occasions we have had unpleasant, distressing experiences with mathematics and we see it as something intangible, something so abstract that it cannot be Connect with us, you don't have to see in our daily lives. And that's why I I think this meme and others are becoming popular How many, right? because of that disconnection that we experienced and perhaps more students from another era than those of us who are here today here, and those of us who have that disconnection. But today I'm going to tell you about the projects that we have carried out, the competitions we have participated in, how There's mathematics, and also... like our experience especially with the Steam approach, with the methodology Steam, which is the application as a whole of science, technology, and engineering and mathematics. When we are students and I see it in My students, we are generating a confusion precisely about what they I was telling you how all of this, all of it These formulas, this great book, eh, that These are Valdor's algebra, by For example, which is still used and many Generations have used it, we can apply to real life. how in my life project, in the dream that I I want to be whatever it is I want to be, I can apply these maths and The answer doesn't usually come to us. Quick, right? We don't usually have Um, that application, so tangible, such that we can demonstrate that We are implementing that. And then we have seen and it has been demonstrated in various studies that show this lack of interest, that generates disinterest, a lack of Motivation, right? And so here it is where the importance of the Steam approach and how we can visualize that union between the different areas and disciplines that we have there. This This disconnection has created a gap in This theory of mathematics and the Practical application, right? Of what We've come here today to talk about how we've had that practical application in the technology and robotics. So, I'm going to tell you a A little bit of history because I'm here today. Uh, I am from and trained in undergraduate degree in systems engineering and I decided to become a teacher more than 14 years ago. It was then on this path that I made something called Coing for Kit, which is One is a training program provided by the government national at that time with different allies. Then came another project, eh of which I am a flag bearer that is She called Steam Girls. This project developed during the year 2020-2021 whose objective was precisely to promote Steam areas for girls, well there are a gender gap in the professionals who develop in these areas. At that same time I was doing another formation that was called Maker, maker, sorry, and something arrived. which was called the maker lab. With My students and I decided to explore that laboratory. You can see images in the second photograph. We went, we took out the kits, we looked to figure out how it worked, we started searching and The alliance also took place with Technocademy, with the robotic part that came into support us. So, we started to build a robot with parts similar to Legos, with devices that are They call them microbits, with an exploration very simple where we had code, But code with a little token, right? What is how does this work? this device from a platform that we have like little tokens that They fit. That's called uh Block programming, right? Where eh We can give different orders and we are analyzing different data from a way for the boys very fun. From there we were in several events, we had the invitation to some national events and we started to to form what they already are today our teams. Initially, uh We had a team that was 80% girls, We also had the opportunity to be children. to present ourselves for some events nationals where we build solutions to problems in our environment, Precisely, uh, well, using it, the tools that we had in that moment. Then, we also entered to be part of a national competition which is about programming and in other events that I'll tell you about later, eh such as what solutions we develop and how how are we applying mathematics invisible, engineering and uh the basic sciences. From there a an event called Ender, which you can see right now, uh, well our image, our mascot and what we have built up to the moment. Ender, code, creativity and community. I'll tell you that in the first At that moment, there were four teams that We were at this meeting in the first version, we are now preparing the fifth version and we've grown exponentially. We project this year There are more than 30 teams that are going to participate. Ender is an encounter where We apply the Steam methodology. The The boys arrive with their equipment from their institutions and form new teams where they meet, complement each other, there are different age ranges, there are different levels of knowledge, of experience and what they do there is solve challenges by station where Of course we must apply logic, mathematics, the resolution of issues. Apply this to assembling, to to program and develop, then robotics. Robotics is the sum of mechanics and programming where we create Well, some solutions, right? Uh, the last photo you can see there It is the last meeting where we gather over 200 people and we've grown Since we started, as I was telling you, with four teams. from the department of Quindío and right now We are accompanied by teams in addition to Risaralda, Caldas and Northern Valle and so I take this opportunity to extend an invitation to Hey, those who might want to join this year and join us here too The doors are open. So we have formed some Smartboots and Cisboots equipment, where eh We meet and work on different situations. So, Initially, let's go to the part basic, to the components, to assemble the robots and from there We began an exploration, to do different challenges where we learn in a very constructivist, very practical program, to move the robots. And that's it. where we begin to find how the guys are looking at these apps the basic sciences in a way invisible. So, for example, We built a robot, uh, we have We use Open Roberta, for example, to to simulate how it will be done move on a track and we start to do the practice. So, uh, we have a track where the robot has to travel a distance. The first practice that What we do is take the time that We set it to travel x distance and the The guys are doing calculations if he They increase the engine speed, eh, for They can do it for less time, if they want. that has a greater reach and they keep doing all these calculations and applying eh of that invisible, intangible way and not mathematics so directly, TRUE? When, for example, the robot has to turn, because they begin to do it experimentally exploring what The tire has to be set in motion, if the from right to left according to the which direction they want to go and how many degrees, because to program we have to do this. So, it's not like We're going to tell them that they're going to apply a mathematical formula to then know how many degrees do they have to rotate tires. implicitly we are doing and we couldn't do it without the basic knowledge that we have within of the normal areas that we are seeing in the different grades of schooling. However, we're doing it this way here. a different way where in a implicitly we are recording how we use Uh, mathematics and other kinds of sciences. For us, for example, it is Communication is super important because We always work as a team and we go building this knowledge and we will by combining these skills that we have because we may not all have the logical mathematical reasoning so developed, but we can have the creativity and in this way in These teams we have managed to create wonderful solutions, superimposed, which we have been able to present in different parts and uh ha has been extremely satisfactory for us. We then have that the Steam areas have has become more important every day. It is estimated that by 2030, 80% of the Jobs will require the skills Steam, right? So, this has had a constant and growing demand to through the years. And of course that mathematics They are the universal language of science and the technology that makes us what we are We apply, right? They are also, as already we know the fundamental basis for robotics and intelligence artificial, which is something that We're talking every day and that That's precisely part of the topic of event in which we find ourselves today. So, the countries have realized that innovation is important. AND Here, as I've told you, I work with I am a teacher in the state, Then I saw how this transformation to precisely seek opportunities on Steam and the power of that way to enter all this part of the global change. That's why they are boosting investments in Steam. and Steam development. So, uh, here's some data interesting where above all I I would like us to see the opportunity that We have, well, according to data and Statistics show that only 35% of Students of the region, we are Speaking of Latin America, they can access quality steam education. Furthermore, as I was telling you, it has detected a gender gap where less than 30% of female researchers Steam are women in Latin America and not It increases a lot at open level. It The important thing about this data is to have in He says there's a great opportunity here, TRUE? that we have a potential of growth in innovation and well, there have been and investments have grown specifically technological education. So, here we have some challenges that that face in order to take advantage these opportunities. Uh, according to tests, the PISA tests, uh only 22% of students achieve a minimum level in mathematics and there is an even bigger gap when We speak between the rural and the urban. Yeah That's why they've implemented it in the government plans, such as them I was saying, then, to strengthen these digital skills, especially the computational thinking in education basic. It's great to know that. We are doing this from the public sector, but also from the private sector. There are many educational institutions that are already with Steam education, with, uh, with all this part of the interaction from different projects, but also many other entities that have to to do with education. We know that the Education is very important for the development and the future of a country and for our life projects. So it is It's great to know that at this moment There are so many resources to take advantage of, TRUE? So there we have one growth opportunity because there is a growth in educational robotics, in the youth academies, the clubs and all this It helps us to promote science and innovation from the regions. As I was telling them and I'm going back to the meeting of robotics, we started with four teams and we were aware at that time of very few and throughout these 5 years that we have been working we have more known, but we have also had the satisfaction of seeing how I have institutions that will meet him, to participate without knowledge deep, because they have already formed youth programs, clubs, and they are progressing also on this occasion which is the Steam education. And so, we in robotics, As I was saying, in different projects, because we apply them in a way invisible and often, well, real and mathematics tangible from the angles, geometry, sensors and the measurement. And for that then, uh, I have a guest who is precisely the Technoacademy facilitator, Rodrigo Franco Luna, who is going to tell us, me It will help to explain a little more here. how we apply in the different projects we have done and from the part of educational robotics, precisely this part of the math Hello, teacher, how are you? Very good days. Good morning everyone. Me Are you listening? Yeah. Oh, well, teacher, thank you very much. Hey, Well, teacher, thank you very much for the invitation, for creating this space for me, Well, to accompany you here in this basic science workshop. Uh, my name is Rodrigo Franco. I I am a facilitator at the Tecnoacademia of Sena and I'm in charge of the line of robotics engineering here at the Tecnoacademia And I've already been doing that with the young people. from here in Quindío, specifically since 2019, because a process of training in the field of robotics and especially since it has been, let's say, like teammate Professor Lina in the terms of e in the robotics experiences that we have come designing here with them. Uh, for me I am an engineer by training. electronics. Uh, however, I had a quite an interesting experience a few years before arriving in Calquindío, where eh where I worked with a line mathematics, engineering, it was called at that time the mathematics line engineering I think the presentation was lost. uh the engineering mathematics line It was, uh, let's say it was in fact... He started calling it that way because, uh What I was looking for was how to put it to use. useful, eh, to mathematics, eh, given a experience that I had already had previously. So, let's just say it wasn't exactly as in the fields of electronics and robotics, but from the line of mathematics we were looking for, for For example, how to get them to apprentices, in our case and students of the institutions educational and will manage to adopt the mathematics, eh, as a useful language for uh implement it uh in their daily lives, obviously, but more beyond implementing it in their daily lives Implement it, eh, for understanding and knowledge of what evil is calls, I mean, uh, hard sciences, uh like physics, chemistry, and other subjects Well, just like this Here in Kindío, specifically in the citizen educational institution of South, uh, in the experience we had in the robotics workshop was very interesting because along with the profelin and to teacher Ana Milena and others professed. We had a good experience Interesting, trying to encourage Young people not only in the use of the programming tools such as Microbit boards, Arduino boards, but we also induced them to do it to identify the need for learn and manage mathematics uh, in order to understand and model uh situations that happened at the level of of eh of robotics applications. So, uh for example, uh Please give me CR7. Just a moment, I'm going to show you a an experience we had And the little black boy is over there too. Ah, no, that's it. Thank you. Thank you so much. So, for example, I'm going to show you two developments, then, that in this They are currently under renovation. Uh, this is a little robot with wheels omnidirectional. That's what we call, then, as a kind of sparring robot, huh, that The idea is that with it we can do Football movements, right? So if you look at the distribution His tires, eh, they're not like very, sorry, it gets lost because they're not like very normal and they see it, they have four tires distributed like this shape. And it turns out that the way to... make this car move in some direction, huh? We have to play with the trigonometric functions. So, you have to play with functions sines and cosines so that the tires uh so that the car can move and Apart from that, you have to play with the eh with the motor voltages. EITHER Well, there are many variables. And not However, these types also arrive of tires, which are another type of tire omnidirectional. I don't know if they reach them Let's see what falls, like this angle more. or less. Yes, yes, this angle is visible here, here, well, here, sorry, like this Like this angle, right? So, from Similarly, that angle also plays a role. uh it also plays a rather significant role interesting. And to understand what it's like movement and how they work and how they are They can move, that's all. through trigonometry, for example. So, that answers one question. quite interesting that they made me a some 11th grade students They are no longer with us at this time, Well, because they're already in the university or are in other processes of training, what good is it to them? trigonometry to them. So, in reality, of course, Much of the math you see at school, except for sums subtractions, multiplications and divisions, They are not used again beyond that point. Let's say, if you're going to perform a basic work activity, but if you transcendent in their training process, Well, it goes even further, it reaches a university or starts doing things like this or choose higher levels of training high, a master's degree, uh a doctorate, for For example, you'll soon realize that... the levels of mathematics that are They work at that point in order to be able to Understanding phenomena is quite interesting. So, in fact, I in Right now I find myself doing a job research a little outside of my area, but more focused on trying to find a methodology that allows me me teach mathematics, but let's say uh as what I, from my conviction, believe which is basically a language and that it has to be taught as we learn to speak. First from the characteristic of the experience and subsequently from the characteristic uh, about formalization, right? Because Well, first we learn to we talk and then we learn what it is diphthong, which is a yato, which is a acute, grave, proparoxytone word, etc. But with mathematics, Unfortunately, well, they can't often not even teach the story behind it. But to Sometimes one understands the history of behind what's in the mathematical postulates, sometimes we are we could understand many situations that happen there. So, well, that's about it. contribution, then, of many of the activities we have done here from the Tecnoacademia as support to the process of of the from the robotics club with profeina. Uh, and well, teacher, I don't know What else should we continue talking about? I don't know, I think I'm lost or I'm live still. Ah, well, well. So, Thank you very much, I had also lost And I think the camera was lost too. that. Ready, ready. Yes, let me know if it's been resolved. the situation. Yes, I can hear you now, and I'm listening to you. I can't see myself. Ready. Well, thank you very much to Rodrigo. Well, uh, as he told them and He showed them, because we have different projects uh where it is very important for us the application, as I mentioned, of uh Concepts like angles, right?, that They are about geometry, time, and speed. AND because we're using it all the time algorithmic logic, in addition to the part of sensors and measurement that all the time, because they also apply math. So, as I was telling you earlier, For us, this whole part is like the we have experienced and as we see that the students can internalize it in a better way. it is precisely with the magic of invisible learning, where all these concepts go applying without realizing it. Uh, and it's very interesting as in learning from mistakes, because it even helps us with these concepts that remain with us as more internalized. So, uh For example, we last year We were working on a prototype of a greenhouse to take advantage of the light solar, to take advantage of the rain. Hey, Greenhouses are found here in the region tomato special and then we started I'm going to do all this part. It turns out that We did the assembly, it worked for us in the laboratory and when we took it to the We had the part where we were going to exhibit it a serious problem because... with the light solar eh the gates h They had a very, very strange movement, but They didn't open completely, and well... We were in the middle of an exhibition, The boys obviously got stressed. because they also said, "We tested it in in the laboratory, we put the light from cell phone, we'd turn on the flashlight and It worked for us. The floodgates were opening when we simulated sunlight. the the of the of raindrops no We had trouble getting it to work, But it was a very frustrating situation. When we returned to the laboratory, So we began to see what the error, the fault, that they themselves They would look. And the conclusion is that the The data I received from the light source is different. to the place where we were, which was a open space, which was also daytime and We at the club work on the evening. Therefore, the programming that we hadn't made for these sensors It was the same, right? the data mathematicians that we had used the we would have had to adjust for the data I was receiving. So, this is what I'm going to tell you, and that Well, I like to emphasize that We use all those things invisibly knowledge that we have, because for to be able to understand this error, to arrive at the conclusion and correct it, because we had to take all those into account Prior knowledge, right?, of the light, from the data that reaches us when we are in an environment, the data that They reach us when we are in another place atmosphere. And before that, in order to do it to program and to be able to put everything together our project, because we had to search for a lot of data, uh, a lot of the Which ones are statistics, right? another part of mathematics to be able to apply to the ideal conditions for the production eh of of what I mentioned to them was the tomato. We had another very nice project for our sector. We here We belong to the Coffee Region. One of the Our flagship products are Precisely because of coffee. Maybe you know him, you have taken him. We have, well, right now, the whole part of coffee of origin, but through the For years there has been a problem with the coffee, what are coffee diseases and This is why we have lost what this is like part of the origin coffees. And then We did a really beautiful project to have a detection of one coffee disease that The stream is called using the data from plant moisture because in the studies that we found this is a determining factor. So, the The boys began to understand more of our culture, from our roots to to access that data, to create this a solution that would serve our environment. Then they started collecting the data, The measurements were taken from the crop and from a very experiential way of taking that shot data, talking to people, from knowledge, because they built a tool eh to detect in a early the possibility that in a cultivation hay hay the roll. Yeah? So, here we go back to what I've... I've been telling them about that use of the mathematics, from what is analyzed, from taking data and, uh, as I was saying also joining in the whole part of the part of the Steam Focus, which are the different areas, right? to think, to to devise solutions, to take what we have at our disposal, like a sensor of moisture to create a solution that can serve our environment. I've already told you a little bit about Ender, So I'm not going to dwell on that for long. But I want to remind you that it is the educational robotics meeting, where So we have a space that is a pedagogical tool where we apply completely for one day the whole part of Steam focus and we seek to promote computational thinking and so mathematician within this, within collaborative projects. Uh, in Ender both participate public and private institutions, We have universities, schools, we have institutions of the rural areas and also the urban areas. Well, with this meeting we have achieved impact four departments along of the 4 years that we have developed it more than 400 participants. all my the experience I've told you about is Well, since 2020, before 2020, well we have sustained a project that we have given that it impacts the lives of our students, of which long after living the processes have gone to training technical and professional precisely in the STI areas and this has been something sustained over time. Now I want to tell you about a project that we love very much, that it is a robot that Her name is Rosita. Rosita was born inspired in robot artists. The first thing What we did with Rosita was assemble it. Yeah, assemble a robot with materials recycled. You see that this first The robot had cardboard. The first thing he did Rosita went to make circles and and because assumed to be making circles then We had to do a whole analysis. how Rosita had to move and turn to make a perfect circle. That was, then, with an investigation. very inspiring because her name is Rosita de in honor of Rosa Ponce de León, who was the first official female teacher in Colombia at the Faculty of Arts in Bogotá. AND So, from there we had some some steps of learning, uh, of learning collaborative, creative, the whole part of programming. As I was saying, we we start e with block programming And it's something we do with the first guys to come in and we're already going moving on, then, to the code itself. And then we decided that Rosita could to be an element that would serve our community in the classrooms. So, uh, Rosita transformed into... that you see, look there, that's built and a potentiometer was added and programmed it to make shapes geometric. And then Rosita took to some transition rooms where The boys had the challenge of moving the potentiometer until one of those is achieved geometric figures, identify them and also identify the color. So, This example shows us how everything... It can be interconnected, right? what I have I've been talking about this for a while, everything that These are the basic sciences, robotics, but also the contribution of our community from the nearest part. Uh, with Rosita, well, we went to a national competition, we were finalists here. So, they are also part of it. from Rosita's beginnings. So, uh, Rosita evolved, we wanted her to It would be better, and then there's a version two of Rocita, because she is also called ADA in honor of the first one who is said to be the first programmer in history and So it's already been modified, it already has a a more sophisticated system, it He built it differently and now We have both Rosita and Ada and We control Ada through a remote control. that we have to that we have because Bluetooth with the cell phone and we take it also to educational environments where uh She's more of an artist robot now because You can draw with it. Are continuous improvements were made throughout the years, between 2023 and 2025 more or less has has been the entire evolution of this project with which different have worked students. Well, as I was just telling you, making mistakes, analyzing the errors, modifying, understanding the logic, applying basic sciences and all the knowledge that we have. Uh, here We have, for example, this year we were with Camila, who's going to... talking, uh, sharing with a group of girls who invited us to a school and They can see Ada that a girl is doing it. So, It is to be satisfactory. Camila has been here since She was very little with us and has been, for example, throughout the evolution of Ada and what Rosita was. So, Camila, who is also connected with Rodrigo, uh I'll invite her for some In a few minutes, she's going to tell us a little bit more so that you know your experience. Camila has been there since the eh from sixth grade, from age 10 in he's in the project with us. Good morning, uh professor, at this moment It won't let us activate the camera, but oh well equal. Hey, Uh, well, yes, first of all, good days for everyone. My name is Maria Camila Velázquez Beltrán. In these moments uh I am currently in my degree tenth, but I started, as the said teacher, a moment ago, I started from sixth grade. I started because Professor Lina, let's say which in a way included us in Steam girls, she gave us that invitation and Well, I actually went in like... curiosity, like no, like yes, because curiosity, to know what it was. And then I kind of fell in love with all of this of robotics and when it began to create the robotics club, like I already did I started to integrate more. And so we in the beginning when it was when It's already started to include everyone, uh, like both men and women, we were many women and really of a certain kind The shape was very pretty because... usually not with no, that is, one He always sees it like in engineering... men and when one starts to kind of women see this as something that It's exciting, it's beautiful. And well, really this Hey Well, yes, it's something I like, I It's something I'm passionate about, and it's something I see too. as for my future because in the end and Cape one, well yes, one falls in love a lot this. Yes. Coming. and from your experience, from What I have said at this moment, of the invisible mathematics, of the application, therefore, of communication and of the other areas you can tell us about. For you initially, how much were you conscious, or how conscious now? You are from the different sciences that We applied in the robotics club in the projects? Well, really at the beginning I never really got to the point of thinking that I was going, I mean, really like that When one hears robotics, one doesn't He thinks it has many areas, but when one begins to delve deeper In this world, well, it's like one... begins to encounter it, that is, like to revive that creativity, Um, like mathematics, let's say it's something that makes one very passionate about mathematics. almost now with time one kind of starts to simply see how easy, as if one really one He doesn't feel that what is difficult is difficult. Well, Cami, thank you very much. porarnosas your experience. Well, uh, here too, uh, Alex is a girl who graduated last year, He also left us a message that... I want to share. Hello, I'm Alicia Pulveda and I would like share my experience. engage in Steam girls and being in the club Robotics helped me learn so much things, but above all it brought me closer to that I finally decide to study. Together My robotics team and I participated in various events and competitions and Everything we did, I would like I want to highlight Rosita and Ada, who were two projects we are working on. Both are working robot artists. as pedagogical tools that They help younger children with their learning processes. What I like most What I like about these types of projects is seeing how other areas can be integrated or approaches with engineering. Rosita was the first, simpler version and with We could see her, like the children, eh They learned about colors, about shapes, and They could also draw while handling it. remote control. Yada was the version improved, which included wheels unidirectional and made it so the Remote control operation was much more easy, especially for children small ones. And that's the cool thing about this guy projects are what can be added many more functions for the children can learn more interactive and dynamic. On the other hand, Working on these types of projects It also helped to see what the Children learned with this type of tools. They not only identify and replicate figures geometric or follow directions like left or right, but also uh they become much more familiar active with technology. and understand that a robot doesn't move on its own, but rather someone who gives him orders. For me it was an experience that was well worth it I'm sorry, and I can say that it marked my life. a very special way. And well, if they He likes programming and robotics, I definitely recommend them. participate and search for this type of spaces to share also with other people what they like to do. Hello, I am sorry. Okay, so, uh, well, uh, this This is what we wanted to share with you. uh within the working group of the group of job. As I told you, I am representative of a job we have interinstitutional and support institutional in education, in the educational institution that I am in, that It is the Southern Citadel. Uh, and then uh With all this, well, we have have been able to participate in national competitions, in regional competitions. As you already know I've counted, we've managed to make an impact four departments. We hope to continue growing, eh, with this moment, eh, of all the Steam part. So we have been in events and exhibitions and we have made an impact with Ender more than 400 participants and already throughout the club that has already been around for more than 5 years, because many students who As I was telling you before, well They have become linked and their life projects They are now being developed in the part technical or vocational training in all these areas. Uh, we can conclude from what we can conclude which are the great results and the transformation that we have seen Throughout what we have experienced, it is that has increased and been strengthened critical thinking, which we work on, but we can also experience and we can see that the boys and girls internalize problem-solving, like Camila I mentioned it, creativity and what we have seen seen in a very Satisfactory is how that has been created teamwork, but how transcends beyond Steam, the science, technology, engineering and mathematics, to that human contribution, that contribution of sharing, in this share, then, create solutions that don't not only benefit me, but also me community, which we also work on emotional intelligence and that then We are after transcending and somehow contributing to the lives of those who people, our communities, to our institutions and in this way We are firmly convinced that we are contributing to the alert of both gender gaps and socioeconomic factors, and then in conclusion We are making a contribution to building the country we want. everything then using uh the basic sciences, the robotics, programming. And then, As a final message, I want to leave you with... Well, learning is the code that... Truth transforms the future. Thank you all very much. Ready. Thanks a lot, Dear Magisterlina María Toro Quintero. Thank you so much for that Nice presentation. I believe we have in the chat on our YouTube channel. Eh eh, they've got them all connected, they're Everyone was very happy about this wonderful presentation you just gave. Have some questions. There aren't many, but while I'm here presenting some of the questions and I invite all participants in the that in the Teams chat, the chat, Sorry, the YouTube chat, do your respective questions, which is the moment so that Dr. Lina can tell us answer. Okay, let's start with the questions that I have been able to gather from in general. Well, Edw Edwin Bastías He tells us, "How easy has it been in your region the implementation of education Steam? Has investment been required? state or regional to implement this methodology?" Well, as I was saying, uh, our Some of our initiatives arise from rooted in some national formations, without However, they are not, they are not situations of vast resources, that is, all of this It stemmed from the training that I personally I had, that Professor Rodrigo had and Others have joined, right?, to a a program, for example, that was called Coin for Kids, which was free to access. Yeah. Uh, the investment hasn't been that big, There has been government investment in the institution as such and we have also I've put a lot in. Uh, I think in this It's largely about willpower. Us The club, for example, we have it in overtime, I was telling them about a mistake that We had to because we worked at night. So, I believe that when one feels passion, He feels the urge, it comes easily to him because The first thing he puts in place is his will and his time. And from there, in my experience Personal, everything evolved, improved with challenges, with that at times We would like to have more than we can have. However, we have managed to do management and as I was telling you, doing some institutional unions that have helped us to have those resources borrowed as it does Technocalendemic, As I was saying, bought, donated. Right now there are some initiatives, some government initiatives precisely for all this, in which we We need to apply, submit projects, count. So that requires our time, our desire. But in my experience, after I Let's put in the effort, everything will fall into place And there are resources available for the person. who is asking which of which They can be accessed from the Ministry ICT, program from Colombia. Hey, We also had nodes of computational thinking, computers to educate precisely He currently has some open calls in especially for students. So It's about taking advantage of those spaces and those opportunities that arise. And also, well I want to emphasize the part human, without the support of the people who They are in those institutions, in the universities, in companies that They have joined us at my institution educational, my own family, so no would be possible. So, I think that's it. That's precisely where that contribution lies. human to obtain those resources physical things that we sometimes need and which I know are sometimes not easy. Well, it's clear that the value added money for these projects It's very important, isn't it? But here we have to emphasize what it tells us, eh our speaker Lina María Toro Quintero. When you put your mind to it, dedication and desire to a proposal Special like this, there's no difficulty that cannot be surpassed. Well, excellent. Well, we have Daniela Silva Sandoval, gives us the first one, the next question. In what way the Mathematics allows robots stop executing basic instructions to make autonomous decisions in environments real? Well, uh, For example, I don't know the scope or what the person who is thinking us is thinking He asks the question, if he's thinking about it. humanoids or is thinking about the robots that we have, because example. So, we have a track on which we have to do a journey to complete a mission. So the clue is to travel along a I walk and take some coins and drag them. We programmed that, We, as I was just telling you, we took We can do some measurements in two ways. ways or we have done it two ways. Um, as I was telling you, a lot because we We made a mistake, and then we rethought the way to do it. Uh, a time of travel with the engine at a acceleration, right? So there we managed to get it to the point after that a mechanical arm is activated and then move in another direction to dragging the coins, which could be a mission. So we all this We do it by taking measurements, eh doing some calculations, testing, TRUE? This is how we apply this. It is programmed, but not automated. Ready? Already. It's a different story when we put tools, for example, of artificial intelligence, where we We enter some data that will be compare, which he's going to take, eh, what we program that takes them so that be automated a function. So, for example, in our greenhouse we had, uh, that a certain range of light provided for it to moved, then, a servomotor that moved a gate or the humidity sensor I had a measurement of this humidity which is ideal for growing that We're talking and then, uh, when is below certain ranges active eh Irrigation, right? So, uh, I would have We would have to look into this, but these ways in which we have Work is scheduled. Yeah? And that's it. we know the same as intelligence artificial because it is the sum of ones algorithms and those who know about We say that programming is a lot, huh? control loops, many yes, do yes, uh, they've gone, well, feeding and because they are already automated to that extent the way we have the interaction day by day day, for example, with the chats generative, which is something else entirely. Ready. Yes, ma'am. Well, here in the The chat isn't just for questions, it's not just... The talk was so interesting that We also have congratulations, for For example, John Cano, congratulations, Professor Lina and her entire team work, especially for those future scientists. Have you considered taking this project to a higher level? national through seedbeds decentralized? Thank you so much for the congratulations, All the credit again to my students, who have been at Over the years, and as I was saying, to all the people who have supported. Well, it's super cool there to tell you what we do now, we are Armenia Steam Territory, which that It has also been an initiative that It was there years ago, but it's a international community and then in In this international community there are some meetings where others are sought experiences are replicated in the region from Latin America. Okay, so I'll tell you that we are fortunate that we were selected to tell our story experience and be replicable in Latin America at a congress, the fourth congress specifically for teachers Steam Latin America is going to develop in Peru this year. So, We'll go to Peru and share our experience. that we are developing in Colombia and We dreamed that it would expand. Uh, well We expect this year, for example, according to What we've talked about, uh, we'll do the invitation to UNAT to come to Ender, we have the Javeriana University of Bogotá that will be linked and we have different entities. So, I think that we are achieving that expansion national. As I was saying, it's something about wills and, for example, to generate resources of their own, each entity contributes its own resources to have their station and the We organizers manage other things. So, I think it's very possible, uh, and we've talked about it and we've dreamed about it that there are regional ones. We need it, and if there's anyone... listening to us, wanting to join and quierac the Caribbean region, another type of regional, very welcome. All the knowledge, all the everything we have The project is built, we can share and we hope that when you go to tell This experience in Peru, so that we may achieve that it also expands to other parts of Latin America. How wonderful it would be, Dr. Lina, to bring her back to be held here at an upcoming workshop, in the seventh edition and that they are recounting those experiences that are going to to be developed there in Peru. Very good. Well, here we have more questions. Here we have more questions. The truth is, it has everyone. participants very active on YouTube. Wow, wonderful presentation. Well, I have Julce Alfredo Herrera. Um, my question The program would be, says José Alfredo. too expensive to be replicated in other regions of the country. It has government support or how does it achieve that sponsorship I would like to know which part of the We talked about, uh, specifically asked a question. However, well, I'm going to... I'm going to to tell in two parts. Uh, we We started the robotics club with things very simple. Microbid. A Micro and You can find it at the market in 150,000 pesos. An Arduino has even a lower value, right? And there are other components through which we can begin. We can start from the Simply put, keep moving forward. As I showed you, For example, Rosita, who was national finalist, it was built with cardboard and supports were constructed in cardboard. We had tires, we had the microchip and a servomotor. They're not very things expensive. However, as I mentioned Right now, well, we've also had the fortunate to have government support national, something that was called laboratories maker, makerlab. Uh, well, we... We apply, we present projects and We teachers also received, we We had to train to be there. Now We have received some resources from Colombia programs that are more microbit, one The wonderful training we had for 3 years. five teachers, we had to commit to studying, to attending conferences in one day, our managers, to give us the spaces to do them, that We have been fortunate and they have us They've been very supportive, and so we've obtained resources that are mostly in materials. Yes, that's the way it is. On the other hand side, Enter, which is this meeting that I have to tell you that it has been so wonderful in us, in the institutions, there's the Sena, there's the University of Quindío, there are schools, Well, of course, Ciudadela del Sur, We put our resources in and go and We set up the station. So, not there. There is significant expense because it is the that we have in the institution, in the institution. We create a problem from the environment and we guide the boys to the We can find a solution with what we have, right? So, as I was saying, it's from wills and unite in different institutions for that we achieve that. And now the part about site management, because normally the we put the same institutions in place site logistics and so we do management also to ensure there is support from private companies and entities governmental. This in fact them I'm telling you that it's a job we do throughout the year at Urban Tender. It We do it in September and October we are starting to manage like the Carnivals all over the country, right? As soon as it's finished, the management process begins. the other. Okay, so, as I was saying, to It seems to me that the main resource Here it is the human being and the will, that we need electronic components and We also need training, but At this moment we have the facility to precisely from these visions global Steam application finds facilities at this time. So, I think that's why What we can start with is training ourselves. But We know nothing about robotics, logic, As I told you, the programming by Blocks is super cool because it's like putting together a puzzle and let's go Analyzing and observing how the cosmos moves, We can start there, and there are some governmental resources and also private resources. We have had the support, for example, of the Conecta Más Foundation, it's their time to Fle Bolie, eh, and that's how we've done it built. Excellent, Dr. Lina. Okay, that's it. We continue with the strip of questions. Uh, Melvin Blanco us The question is, how does engineering influence systems in robotics? S. Uh, systems engineering, like we know, in systems engineering I think it's something wonderful because in systems engineering We learn many branches, right? No are we only focused on the software or in the electronic part, but it is precisely one of those careers where We link everything. So, uh, it has everything that we see developing robotics. We need to have the capacity to analysis, design, creation, that which the We systems engineers see it a lot, TRUE? analysis, design, planning, execution, trial and error. And that's what We do it all the time in robotics. We also program for robotics, Therefore, we apply logic algorithms, programming logic and Well, I'm talking to you about programming because blocks because it's the part I like the most I work with children, but we've had projects developed in Arduino or already in programming languages ​​such as Python with databases, the part of Machine learning is already being worked on also more in programming and that We are exploring some projects there, Well, we've already made more progress with the construction and code development. which is a little plus the focus, but within the of the which is the basis of systems engineering We apply it completely all the time. Identify the problem and analyze it, design the solution, plan it, build it and test it. We do it all time. Ready. It is clear here that the systems engineering plays a role very important in these projects, right? It is what allows the development of these projects. So, every day the Systems engineering leads us to things more interesting. Okay, Dr. Lina. Here Hugo Ruano asks us, there is already students or participants in YouTube that are partly interested of that project. Then he asks us, How can we access or connect to projects from other cities and how can we carry out our own projects? S. Uh, we have social media, uh, We have Ender Encuentro on Instagram Robotics, we have the email ender@udaladels.edo.com. I think we can leave them in the YouTube comments. I'm also going to to leave my personal email. Uh, they can go to TikTok and Instagram and look for us. There you'll see more than what We do and are willing to to receive, so that they may come and live. As they He said, "How cool that they come and live here." part of what we do here and it can replicate in the other regions that today They are watching and listening to us. They listened to all the participants, No? Hey, keep an eye on the social media of this great project so that also Bring your ideas and develop them. AND What else? with the support of Dr. Lina, who already has a significant presence in This type of project, and well, it would be a A very important guide for those who want to begin in this branch of robotics. Okay, then, John Brandon Dominguez He asks us a question. How Mathematics allows robots stop executing basic instructions to make autonomous decisions in environments real? We had already answered that. It is the Yes, it is the same. Well, So that question has already been answered. evacuated. Let's move on. Ask Ivandarío Science, could a project industrial? How to make schools or universities start more early in this form of learning? That's super cool, we've done that We've spoken, and I think we're making progress. with the universities of how in the the pace we're at right now historically significant in the world, it becomes necessary that the university gets closer to the school, get closer to the average, to the basic, uh, and there are some approximations. I think the first thing is there and no only for us who have Well, with electronic engineering, software engineering and mechatronics alliances, but for different engineerings that we know, as it We were just talking, uh, can you interconnect in this type of project, Well, those alliances are precisely so that these spaces exist of construction, of meeting and of knowledge. That's precisely what we're doing. measurement in the engineering section electronics with the people of the University of Quindío, because they have observed that since they have linked to Ender have increased the registration number for your race, TRUE? So, we're already there. by systematizing and soon we will have more scientific and official figures. But but we have been able to demonstrate that bringing spaces closer, that sharing It nourishes us in the interest of the students and that they think about their life project in being for some of these branches. and in my opinion it applies For many areas of engineering, no as I mentioned, systems electronics, no, for many areas of the engineering, because we know they are interrelated and that also all eh We are currently in the construction and especially in the innovation, in and in the exploitation and the management and development of tools that are so prevalent, huh like AI. Okay, we're almost finished. our question session. I have a Nelson David Junior says that if we Could you please give one? analogy, a comparison with examples practical applications of mathematics and physics in everyday life, but with examples non-typical practicals. Uh, practical, not typical. There are so many, right? So, there I invite you to think. Uh, if in your city, Where it is, it crosses a bridge, in the construction of the streets of his city, somewhere there's a bridge. So, I invite you to think about what precisely We applied to build a bridge and I I am referring, then, to the meme with which I started This talk, right? There we use the trinomial. For example, I believe that in everything We are currently applying the mathematics, as I was saying, in a way invisible. So, the person The person asking may have expenses Daily, right? And apply the rule of three to find out how much you can spend Today, if we can go and get ice cream, to eat the coffee and cake, but also is applying something as simple as a subtraction, which is mathematics. Yeah. Uh, and we could continue talking like this. all the time, but only us We have this little computer with us all day long. In our hands, right? that that is The port has become vital and supremely important, then, so that we can The signal arrives and there's Wi-Fi, which Furthermore, those mathematical calculations A woman there made a hat for me. gender flag, uh, well there they are You are applying, you are interacting with them in the in the measure of the food you eat Rice in Colombia. What is the formula for rice in Colombia? One part rice to two parts water, right? That's it, I think we should put on the little bags. of magic and see how it all works that surrounds us, there are principles and there are applied precisely in the sciences basics. Ready. Thanks a lot. They were not I forgot the formula. here one where we are broadcasting that sixth science chain workshop basics. Closing remarks for this presentation. Okay, thank you very much, Alexis. Well, I would like to thank Professor Lina Toro for share your experience with us from Armenia, by sharing with us everything that all of his experience with Ender, with uh everything which has to do with the program of girls in programming, uh, that's... an initiative that also links much of the public policy aspect that which precisely the departments and everything related to the sector education and government should always be very linked to this type of project for which could also generate some important results, right? What is that it be precisely like an orchestra that we all, well, aim for the same thing symphony. Uh, I also see a lot of Congratulations in the YouTube chat, Very interesting how mathematics They can be a stronghold in the field of robotics. and its impact on the institutions. @danielaprendizaje also tells us, "Me They like the testimonies of the participants, in my case I like the mathematics, but there are too many formulas, concepts, or notations that give the feeling of getting lost and existing easily, as he was telling us Our speaker Lina, uh, see you now Well, mathematics also from another perspective. optics, well in this case, uh, uh, to learn mathematics using programming and with robotics. Interesting. @Hugorano tells us, "How can we?" Well, they didn't read that one. Hey, @sergiodurán He tells us, "Robotic electronics can to impact all fields, in especially in agriculture, starting from the use of sensors, the desire to control variables such as temperature, etc. So, Professor Lina, Thanking you very much, we are in communication as well, because we expect to have it in other versions of our basic science workshop. Thanking the eh for their presentation Hey, speakers who are joining us, that We were accompanied by Professor Lina. So, thank you very much as well. Well, to the students who contributed for this presentation. Thanks a lot. This last comment about uh the agriculture and everything related to it also with this robotics component, electronics, mechanics, uh, it's going to open us up Moving on to our last presentation of the day today. So, I'll leave you, Alexis, with the presentation. Thanks a lot. Ready. Thanks a lot. Well, before to give way to the next presentation, I want to give you many Thanks to Dr. Toro Quintero. Very enriching everything that has happened to us shared this morning. The experiences of his students have been very enriching. We hope to have again with your valuable presentation in future events organized by the basic science chain. Well, So we'll continue, right? Daniel? On the second try, on the third try presentation of the day. Ready. Okay, so let's start with the presentation on research seedbeds Matinnova. As part of strengthening the formative research we have participation of our youth workers. This time they share their job. Well, we are accompanied by the Brini Dayana Rendón Toro, a seedbed member student leader, facilitator from the Matinnoa research group. Brinny Dayana is a student of electronic engineering at the University National Open Distance University UNA and technical SWAT analysis under development Sign. Their supplementary training includes C++ programming Google Hall Computing, Automation industrial, electrical installations and application of sensors in circuits electric, which has allowed him consolidate its solid profile in the intervention between electronics, the programming and control systems. She serves as a student leader. facilitator of the Matinova seedbed, attached to the logic curriculum network, Algebra and Calculus at the University National Open Distance University UNA, where develops research projects training focused on analysis mathematicians of technological systems. In September 2025 participated as speaker at the national meeting of seedbeds research and at the meeting of research, innovation and projection social event held in Palmira with the design and implementation work measurement systems of variables soils and data analysis in cultivation AS avocado in Sonzón, Antioquia. Today He presents his paper entitled Analysis. of the sensor foundation in the system of telemetry from the perspective mathematics. Go ahead, Brigip Dayana, the The space is yours. Welcome, Alexis. And let's give it 5 minutes, uh. Please wait for Brind. Ready. So, we had a little technological problem. Yes, yes, I already did it We're going to find a solution. So, We'll wait a little while, 5 minutes our seedbed Brini. and Okay, let's continue with our third presentation and final presentation of this day of the mathematics workshop of sixth workshop of the science chain basics of the National University Open to Distance Learning. The presentation that It continues, titled with the name of analysis of sensor performance in telemetry systems from the perspective of mathematics. So, I'll give way to Brilliayana, eh seedbed of the seedbed of investigation. Nova. Go ahead, Dayana. Well, good morning everyone. Me Please confirm if you see me. correctly and if they are watching correctly the slides. Ready. Uh, good morning. Let me introduce myself Again, as the teacher had already... My name is Brignana Rendón. I am part of the undergraduate engineering program electronics, and in this case, well, I come in representation of the Matinnova seedbed as a dynamic leader. In this case I'm going to talk to you a little about the subject matter What we are going to address is the analysis of operation of sensors in systems telemetry from a perspective mathematics. Uh, first I'm going to do a... little about the recognition of hotbed. It is very important for the attendees who, in addition to learning about various topics, in this case different basic sciences, we also Let's soak the seedbeds that we the university is offering it, and well, yes are interested in being part of they. In this case I'm going to talk to you about Matinoa seedbed. This is a seedbed who is attached to the School of Basic Sciences, Technology, Engineering at the National Open University and Distance. Uh, we're affiliated specifically to what is the eh zone south-central areas. The working core Basically, it's based on this whole topic. research and development of eh pedagogical strategies that are innovative and that can be used for eh the teaching of mathematics. Let's say which as such we don't have very good lines certain and we hope that with the over time these can be expanded lines, but we can talk first about what artificial intelligence is and data science, where we apply, For example, what is the machine? learning, uh, data mining. We also have what are the STEM technologies, where we develop different technical solutions through physical models, modeling mathematicians. We also have, like I was talking to them about the topic of innovation. educational, where we design different resources uh for let's say to fill those learning gaps that These virtual environments exist. Also How were you all? Uh, let's say the center From the heart of this seedbed is develop different skills investigative. Eh more than anything else We are, let's say, directing in what It is the management of scientific networks. Hey technological surveillance, uh, let's say the bibliometric analysis, to know about this whole area What scientist is happening with different topics and also writing under international standards. H we can say that Matinnoa relatively It's a very young group, it was formed more or less about a year ago, but still So, let's say it has different verifiable impact indicators. We have what is second place national in the Latin American Real Innovation in the impact category social. We also have what is a constant production of different working papers, from different projects and we have taken these projects to different presentations, both within UNAT as it were. For example, what It's Spotage that we participated in last year. past and the zonal meeting of seedbeds. we have addressed different themes, we have then as different open projects within the seedbed in different themes, for example, What is agro-environmental monitoring? different, for example, systems for what is failure prevention academic. Currently as a seedbed We execute, uh, let's say, or we have a very robust agenda. We have what is uh The international congress is coming soon. of mathematics conferences interactive sessions, which we also invite you to attend to be, let's say, aware of the university channels so that can also participate in these other events. And I also tell you that We have several different teachers, We have a team of teachers and students, it's a team interdisciplinary. Uh, let's say we have, uh, uh, teachers that they are giving us different information and that they have different knowledge in many in many areas. Uh, by 2026 already We begin, let's say, with our outreach and technical training. Uh, one of, let's say we could say that one of the sessions This one that we are going to present in this sixth basic science workshop, but We also have other classes that can to participate, let's say, people who are directly linked to seedbed, but they are outside. By For example, we have different sessions in Regarding reference management, standards APA, scientific writing, analysis, Let's say, data. And well, then after having them told a little bit, well, a lot about seedbed, uh, I invite you suddenly the Call to join Matinnova It remains always open for students, not just students who belong to the school because basic sciences, technology and engineering, but students of technologies, undergraduate, meadow, of postgraduate students and even graduates who want to belong, eh, no to our hotbed. In this seedbed no We don't need any kind of experience. We can say that this seedbed is like a training school from scratch, in where we get different support teacher, for example, for projects of degree, for personal projects, uh the possibility of being able to obtain different certifications, or let's say if any of them The people who are here, uh, think, "I would like to participate, for example, in all these events." eh join to our seedbed or one of the seedbeds that will be touring Well, the workshop is happening these days. It is a possibility for you not only to remain behind the screen receiving all knowledge, but that they can develop their own projects and can take them to expose it, to share it with other students. So, I invite you if you are Interested parties should contact our leader, Professor Daniel Steven Morán. Uh, and also, well, if they want, uh, let's say Refresh what I'm telling you, You can consult our microsite which es matinnova.github. Uh, about what I told you a little bit. Let's begin then with the topic as such. Uh, we see that from what they I spoke, the title of the proposal has many components, it has telemetry, It has sensors, it has perspective mathematics. So, let's begin from the most basic level to reaching that mathematical perspective which is therefore as what brings us together today in this tomorrow, which is like the space that we have in mathematics for this workshop. So, I'm going to talk a a little bit of telemetry. Basically, the Telemetry is a technology that will to enable measurement, acquisition and the transmission of data over a distance without need for a person to intervene directly at the place where it is generated that information. Hey, let's talk a little bit as such regarding the word telemetry. This comes from the Greek tele, which It means distance, and from the Greek metron, which means measure. That is to say, literally the word telemetry It means measuring at a distance. There we saw a little bit about what it is, about its word. Uh, we can say that the Telemetry dates back to roughly late 19th century with the development of the first systems both electrical and communication systems, for For example, the development of the telegraph. In These systems then began to transmit basic information to through different electrical signals. So, these developments those foundations for what we know today such as modern telemetry. During the In the 20th century, telemetry already had, Let's say, a significant advance rather than everything in what were the sectors industrial and energy sectors, especially when it was needed monitor, for example, networks electrical, where it was necessary that the people knew different variables such as voltage, such as current, and that These variables were taken in real time real and that they were sent to centers of control. Uh, one of the impulses within from the development of telemetry occurred in the aerospace field, which in this Then it regained its fury. Uh, it was particularly applied, let's say, in very important applications. Them I could mention the Polo program, if Some are not very well informed about these missions that have been done within NASA. Basically the Apollo program It was that set of space missions uh that developed uh within the NATA approximately between 1961 and 1972 with the objective of, let's say, bringing human beings to the Moon and be able to bring them back back safely. Uh, in this The Apollo program was needed then monitor different parameters such as temperature, pressure, speed, state of the systems and all this could not monitored from the same ship, but that needed to be monitored from the ship, but that data were transmitted to Earth. Hey, In this context then, telemetry It becomes fundamental, since it allowed, Let's say, receiving that data in time real and make critical decisions for the security, in this case, of these eh aerospace missions. Uh, with the progress then of what It was, let's say, electronics, the telecommunications, because we've already seen it all. in the other conferences that all It's almost related to everything. So, With the advancement of electronics, the telecommunications, also the systems Digital telemetry evolves even systems that were much more complex and much more efficient. Then, new sensors are integrated, They are also integrated microcontrollers and are integrated communication networks. Currently with what we know about the development of Internet of Things, or what we call IoT, telemetry has become This technology is essential in multiple areas, that is, we see it reflected in the What is smart agriculture? medicine, industry 4.0, for example, smart cities and almost in all the applications that we uh Let's imagine ourselves in all these systems. So, I'm going to mention that the sensors play a role fundamental, since these are the responsible for taking those variables physical aspects of the environment and then to process and transmit them by mathematical models that will allow your analysis and understanding. We continue. Then I mentioned to them that, Let's say, it also appears a little here. about what the Internet of Things is and in many areas, or let's say we can confusing this aspect of the internet things and telemetry. Uh, let's say which are often confused, but These two have very different differences. important. When we talk about Telemetry, this is a system that is focused primarily on measuring variables and send that data to another place. Uh, I mean, the function The main point of telemetry is that we can acquire the information and transmit it. On the other hand, when We are talking about the internet of the things or IoT, this uh tends to be a a much broader concept where In addition, we included the part about telemetry, we also incorporate what It's internet connectivity, uh, because For example, what is the processing of data, cloud storage and Let's say that in the IoT field as well It is part of what is the possibility of make decisions and be able to control different devices remotely. So, in other words, we can to say that telemetry is a part fundamental within the internet of things. For example, I'm going to give you a example. If we have a sensor temperature you are sending data to a receiver, in this case we would be talking about telemetry, but if that same system of temperature is already connected to The internet already stores data in the cloud. and it already allows us, for example, to activate an automatic irrigation, Well, then we'd be talking about what it is. the internet of things. So, From an engineering point of view, Telemetry is the most basic form of data collection. And we can see So, for example, uh, we can determine that the internet of things It could be an evolution of what we call traditional telemetry because it involves other technologies advanced. Suddenly, hm, they begin to doubt what exactly can it measure? telemetry. We already saw, for example, in the Apollo program, what did telemetry measure, But what else, how else could I do it? apply. Well, I can tell you that Basically, telemetry can measure any value eh of a physical variable that can be captured by a sensor. That's why I was just talking to you about the importance of the sensor. For example, in different common applications we can to measure, for example, what is the temperature, humidity, pressure, the distance. But when we talk about systems of Soon, a little more advanced, we can... measure, for example, I don't know, variables biomedical, for example, the rhythm cardiac, the oxygen level in the blood. So, uh We can see that there are many measurements. that can be done with the telemetry. Something very important is that Telemetry doesn't just measure one variable, but it could measure a single variable, but it can also measure many at the same time time. For example, I was talking to them, in the The Apollo program monitored variables critical factors such as temperature, pressure, the fuel level, general condition of the ship, for example, and all this Information was being sent to Earth where different engineers or specialists, uh, of, let's say, this airfield could take real-time decisions. So, we can see, uh, let's say the difference between what was the Apollo program, the Artemis program. We can see that in that moment the Apollo program uh when We're talking about control stations of the Polo program, these were mainly analog systems where a large part of the The analysis depended primarily on human operators who were interpreting data. Now, if we We compared it to this new program, I don't know if they're aware of it too, that a new one was recently carried out moon landing program that was the Artemis, uh, when we talk about In telemetry we see a very significant evolution significant when we compare the telemetry in these two processes of trip to the moon. Today in this Artemis program, in addition to those basic variables that I already told you about They were monitored in the Apollo system, Different ones are also involved, We can say it, digital systems much more complex, for example, what It's advanced navigation, the conditions of the spatial environment and other something that was included in this new The program's objective was to be able to analyze data biometrics or detailed health data of each of the astronauts. Can So you see that they not only changed, Let's say, the sensors, because The sensors are probably already... better quality, for example, and the amount of data that was collected, but that also change the seasons control. We can see the station of control that is on the left, uh, of the of the Apollo program versus the right wing of Artemis program. Uh, currently the the Artemis program station is a fully digital station. uh that It contains systems capable of processing large volumes of data in real time real and where humans no longer intervene directly to the analysis of this data, but this analysis is supported by different algorithms, by different automation processes, which It then allows decisions to be made. faster and more accurate. This demonstrates that, let's say, evolution telemetry data during all this time not It's not just about what it's measuring, but which also depends on how it is processed, how the information arrives and how The information is obviously interpreted. Well, we also talked about what a a little about why it's important telemetry, especially in the field of engineering. In this case, the Telemetry has, let's say, a role fundamental in engineering because it allows us will allow obtaining information in real-time of different systems without need for direct intervention. That The most important thing was, well, as with the Let's start this conversation. That is key because, well, let's say that nowadays Many processes will require monitoring constant to ensure its correct operation. For example, uh, I know that maybe it's from the people who us They are, uh, they are with us in this workshop via YouTube, we have students or perhaps people who have knowledge in different areas, then they are asking, But what do I have to do with it? telemetry. Telemetry is that which It works over there on the Polo program or in very complex systems, but the The truth is that telemetry is implicit, it is within many of the processes. For example, I don't know if in the chat, uh, is there, let's say, someone who is handle the industry part. In In this case, telemetry is responsible for the whole supervising part, uh machinery, detect faults, optimize production processes. I don't know if suddenly Is there anyone in the chat who specialist or who is studying eh within the topic of the health area. In this case, telemetry in the area The health sector would allow us, for example, monitor vital signs both directly as well as remotely, something like that, huh? So what do we see inside hospitals? even, for example, what is the home care. No, you do. For example, maybe there's one in the chat person who is within areas of agriculture, well, all these areas, uh For agricultural and livestock purposes, we can use, For example, telemetry to measure the which is soil moisture, the temperature and other variables that may uh help improve, let's say, the crop conditions. Also We have what is, for example, the energy sector, those who already have I had, let's say, said, where it was It is used to monitor different networks electrical, control substations, detect faults. For example, when we talk about transportation, we allow what is the monitoring of location, speed, the condition of the vehicles in time real, eh, and it can be applied in different components, such as in logistics systems, in transport public. So, we can see that the The application of telemetry is in many aspects of life, in many professional and personal aspects of life, and that it's not just, let's say, a word or a technology far removed from but it is implicit in us many of the processes we all do the days. Something very important is that all that information that they generate These telemetry systems not only They use it for monitoring, but rather let's say from telemetry, of this basic process of collecting data new ones also arise technologies. For example, when We're talking about intelligence. artificial, artificial intelligence It uses data that, let's say, it takes and through them you can learn, Let's say, patterns, making decisions automatic. Telemetry also provides information, uh a step towards an important technology today in day that is the elis the data analysis. In this case, where this technology This allows us to process large volumes information so that we can, by for example, finding trends, detecting Failures, well, optimize performance of systems, for example. So, in In other words, we can say that the Telemetry not only measures, but also generates data that they will then be able to feed different intelligent systems. So, up to this point we've talked about a a little bit about what telemetry is. Already Let's break everything down a little bit, okay? that I have prepared for you. And that's it. We're going to delve a little bit into what What is the sensor? Remember that already we had talked a little about the sensor. So, um, to understand, Let's say, what is telemetry, First we must understand what a sensor, what role does it play within the system, for example. Anyway, the sensor then that would be the starting point of telemetry because it is responsible for to capture information from the environment. So if we don't have a sensor, because we have no information that capture and therefore we would not have data to transmit. Let's say a sensor could work like a transducer, which means that will take a physical variable, such as for example, temperature, pressure, the distance. And this sensor will... convert into an electrical signal that goes to be interpreted by a system electronic. So, this signal then is transmitted, then processed and It will then be analyzed later. within a telemetry system. Hey, So the sensor is that interface between what is the physical world and the world digital. Um, within the sensors, let's say that we can make a classification. The Sensors can be classified as different forms. One of the most important forms of classification of The sensors depend on the signal. that they generate. First we have what is analog sensors. These generate signals that within the field of In engineering, we call them signals. continuous. That is, uh, for example, Let's call them values ​​that go changing shape smoothly. Uh, an example that we can imagine at this moment is when we have a volume knob. We can go up or we can go down the volume gradually. We don't We need, or let's say the system doesn't It has two limits, saying I can only can I leave the volume at minimum or can I only not leave the volume at maximum, but that The volume can have different values. levels. That's how they work then those analog sensors. Uh, by For example, uh, let's say, uh, the sensor LM35, which is a temperature sensor, He's not going to tell us directly We, it's not that there is a presence of 20º, is that there is a presence of 21 gr, but that this sensor will keep changing the The signal it gives us depends on that temperature change. On the other hand So, these are the sensors. digital, which would be like the unlike analog sensors. These work with, uh, what in what we call engineering as discrete values, that is, steps defined. For example, a very an everyday thing would be a switch. Us When we flip a switch, it can it can be switched on or it can be switched off light. We use the switch we cannot, let's say, vary the brightness of the light bulb, but rather... It therefore only has two states. So, That would be the difference between those two. types of sensors. Analog devices can have different types of levels, different types of values, but the sensors when they are of digital type They can only say it's on. It's off, uh, is there a presence or is there absence. Uh, another way to classify The sensors depend on how they work. Uh, we have what are called sensors assets where these need uh that We feed them so they can operate, They need external energy. An example It would be, uh, an ultrasonic sensor that will need energy to be able to emit that signal and then be able to do the measurement. Instead, we have what is passive sensors as well, where These do not need external energy to generate a signal. For example, when We have a solar panel, uh, the panel is going to receive the light and will generate electricity by itself. He didn't It needs, let's say, external energy to work. So, uh, we can say In summary, this classification tells us helps to understand initially from very fundamental steps how to The sensor works and how we will be able to to process the information within a system, in this case, telemetry. Now, if we move on to what is the mathematics, probably some are saying very interesting, others perhaps perhaps it's not from, let's say, inside their interests, but the question here What stands out is why this topic within the workshop in basic sciences and especially within this field of mathematics, what do they have to do with it Mathematics, huh here? So, for analyze the sensors from a engineering perspective, in mathematics, is fundamental It is essential to understand that the functioning, and I know this is a The phrase, already very overused, the functioning of the sensors such as the operation of almost everything, it is completely based in mathematics. So, we can say yes, in almost the entire workshop, at least in this tomorrow we dedicate ourselves to the mathematics, they've told us, "No, it's that This principle is based on mathematics, What we have done is based on mathematics, but perhaps we that's all we're left with. There is mathematics there, but I don't go in too deep. I don't know what The formula applies, I don't know how it's done. I I know there's math involved, but As long as it works, everything's fine. So, today I'm going to share with you that in Regarding the sensors, we can do a mathematical modeling in different aspects, that is, we can model different aspects of the sensors by through mathematics. So, in First, we name what the modeling and calibration. In this step, This establishes that mathematical relationship. between the physical variable that is entering the sensor and the electrical signal that is coming out. For example, I go back to another example. When we have a sensor Regarding temperature, there is an equation that It will tell us, for example, how much changes the voltage that it delivers to us sensor depending on how many degrees rise the temperature or by how many degrees go down. So, this would allow us, therefore For example, this isn't just because, because it describes how it works, but This would allow us, for example, adjust the sensor so that the measurements are correct, so that we information that truly arrives be useful. Then we have, for example, resolution and range modeling measurement, uh, where the resolution indicates that change is smaller than the The sensor can detect. is similar or I I'll give you the example of when we We have a rule, and that is that while the rule more divisions have, we we can make a much more accurate measurement precise. It means we don't We will always measure in meters, in centimeters, in millimeters, but while the units are much more small, because that measurement is going to be much more accurate. In contrast, when We're talking about rank, this range will define both the values minimums as well as the maximum values ​​that a a specific sensor can measure. Hey, Another key aspect could be, for example For example, signal processing. It can also be modeled by means of mathematics. So we know that The signs are real, aren't they? When we are, let's say, simulating them in some software or that we are doing it in a controlled environment, when the The signals are in a real-world environment, They will always have different noises, different types of interference, Therefore, we are going to use, Let's say, different tools math. A mathematical tool to control those filters, those noises These would be the filters. These are used basically to clean the signal and we can obtain much more data reliable. Uh, there's another part too. from which we can model Mathematically, it is the fusion of the sensors, where we can combine eh data from multiple sensors using, For example, probabilistic models. And finally we can model what it is the dynamic analysis of the sensor. In this In this case, many sensors are not responding. Let's say, immediately, in a instantaneous, but the output changes over time. So, uh, for us to be able to describe this behavior, We also use different differential equations, functions of transfer, for example. So, In summary, we can say that the Mathematics allows us not only to measure, but understand how it works that device for later we to get involved and be able to improve and optimize how those work. We move on to what is modeling mathematical then of a sensor. In As I was saying, the behavior of a sensor can be modeled mathematically by means of a function that It will mainly relate what I have at the input, that is, the variable physics with what he's going to give me sensor at the outlet. This is They consider different effects such as the sensitivity of the offset, of the noise, the temporal dynamics. Uh, then we can say that for us to understand how a real sensor works, no It's enough to just put it on or say, "No, it's that this sensor measures temperature, that's what this sensor measures pressure, but if we do a analysis within engineering, within of mathematics, much more complete, can we know mathematically What's happening inside that sensor? so that it's giving me the result that is throwing me. So, uh Likewise, the sensor takes something physical and It converts it into an electrical signal. Is In other words, every measurement we see is not a It's not by chance, it's because that's how it is. They designed it, because electronically that way It is, and I'll leave it like that, but uh, it's product the behavior of a sensor is the product of different equations mathematics that will model each one of behaviors. Now we're going to break that down into parts because uh We talk a lot about mathematics, As I was saying, mathematics They are present in everything, in what a good way. in which we use mathematics, in which We use geometry, well, the different branches of mathematics, but We didn't really delve into how I can model a behavior through the math. So, today we're going to I have seen represented by means of a sensor. The first thing we're going to model is what It is the basic relationship. So, first Let's focus on the basics. Yeah We, uh, if we have something like what it is, uh, let's say the temperature, the sensor, let's say, goes to convert into a voltage. This It means there will be a relationship direct connection between what is going to enter the sensor, which in this case would be the temperature, with what will come out, that In this case, it would be the voltage. For example, if The temperature, for example, rises, the The voltage will also rise, thus determining that it was a sensor that, let's say, works linearly, that if the temperature rises, the voltage Get up, okay? Then we can say, Let's do it with that example, the The temperature rises and the voltage rises. So, that relationship we have between We can find the entrance and the exit. describe with a simple equation as the one I'm showing you. So, that equation will represent how the The sensor will convert a magnitude physics in an electrical signal. Hey, So, basically, the equation... What he's doing here is modeling the behavior from the most basic form from a sensor. In this case, the variable X we can determine like what I want to measure, for example, What is temperature? Well, it's going to depend, then, on what I get, for example, voltage. Uh, the variable K is going to determine what It is sensitivity. In this case, the Sensitivity tells me how much the changes output with respect to input. And for Finally, we have what is in this basic relationship equation, we have which is variable B. In this case, uh We should take this as an initial mistake, because For example, when a sensor registers something even if there is no signal. So that The equation works because, let's say, Many of the sensors have a linear behavior. As I told you, This could be one of the most... basic, but we still must, Let's say, to get a little bit of an idea of ​​what it's like that each of the sensors works to determine the basic relationship. We can say that this is not a basic relationship that is applied in not all types of sensors, but We can have different ones basic behavior modeling depending on exactly what you do each of the sensors. After We involve another model, in this case It would be where we involve the aspect of the noise. So, as I told you, in real life, generally speaking, Measurements are never perfect. There are always different variations, different interferences and that's what that we call noise. By For example, so that they can know better from what I am to what I am referring. When we say We talked on the phone and there interference, we don't hear perfect. So, that means that The signal is not being transmitted from perfect shape. That's exactly what happens with the sensors. The signal we get It will always have small ones alterations. So, we can see that Hmm, this noise equation I have here It's an improvement, or yes, an improvement on what is the basic relationship equation, in where we already involve that component of noise. So, here we add the noise component, which in this case we represent with ndt. Um, I don't know if from Soon someone will be wondering why What the noise in this case adds to which was the appropriateness of behavior general. In this case, uh, we can say that the noise is not that we are going to have a separate noise signal and a a sign, let's say, of what we are measuring separately, but the measurement The final result we obtain is a sum between the actual signal from that sensor and the noise. So, That's why we, let's say, We integrated this noise component also to the behavior of the sensor. Then we also do what is the Delay modeling, which is also a important component within the sensor behavior. Uh, there are Something very important is that the sensors will not always respond immediate. further. I would say that in the In most cases, they do not respond. immediate And I'm going to show them to you in the following way manner. For example, if we put Um, let's say a thermometer in water hot, that thermometer won't tell us to instantly display the temperature, but this thermometer is going to take a few seconds, probably until minutes, depending therefore on the quality from that thermometer so we can give that temperature measurement. So, that We can also adjust the response time. we represent through math. So, in engineering We use a constant that tells us what That sensor is going to respond so quickly. This is key because in systems, when We have real-time systems, We need to know if the sensor is fast. or if it's slow. That is, if what We are seeing it reflected, uh, if the measurement that we are Seeing it reflected does correspond to that moment or the tensioner is like a little either behind or ahead of schedule. In this case we have that equation in where the term y over t represents how quickly the output will change. Uh, you mean how fast it's going to react to that sensor in response to that variable physical, environmental variable, as it want to call, to give me the go-ahead. AND We also have in this equation what is the variable, the variable t, which is like that rare little piece of land we found in many of the mathematical equations and It will tell us how slow or how The sensor is responding quickly. So why this equation? This Basically, what the equation does is modeling first-order systems. Hey, First-order systems are very eh common in different physical sensors. Um, as I was saying, it's very important We need to keep in mind that there are many types of sensors. What's more, uh, Let's go back a bit in the slides when we were talking about sensors. In this case we can see that There are a lot of sensors. We have, therefore For example, a color sensor that will detect, because obviously different types of color, an alcohol sensor that, for example, when we that they drive and so on, when the police Traffic officers stop us to do different breathalyzer tests, because They are most likely using a alcohol sensor like these. Hey, We also have, for example, the gas sensors that measure different eh types of gases in the environment. Have sensors, uh, let's say when we live in a closed set or spaces closed, this, for example, a sensor uh that detects when a person is smoking, as it can activate other protocols to prevent fires and others. We also have, for example, light sensors, proximity sensors, which is a sensor that will measure how much How far is there from e to the sensor? towards the object. We also have, for For example, here we see the LM35 sensor, which It's the temperature sensor we installed Let's look at an example. We have a sensor rain, which is what's going to... to detect if it is raining or not, what There is so much precipitation. Have ultrasonic sensors that work also in a way, like, uh, like in within the principles of a sensor proximity, we could say that. Hey, We have a touch sensor, a sensor of ambient humidity, in this case this down here, that little blue thing we see. We have phototransistors, gyroscopes Also, they are different sensors, eh that measure the position of an object. And finally, here in this image We have what is a humidity sensor. on the ground. So, we can see that There are many types of sensors. So you are probably asking, whether that modeling mathematical that we did when we speak of a basic relationship, when We talk about noise, and when we talk about The delay will always be exactly the same. So, right? It could be a, uh, let's say that I'm giving you an example of how it is I could model a very basic system of sensor, a linear system, a system that suddenly, uh, doesn't have much complication, as I was saying, because For example, one of temperature that I simply reacted, depending on the temperature, because it will change voltage. The higher the temperature, the more voltage. For example, this one We involve noise, to this We involve delay. So it is important. Hm. I believe that the colleagues who are here inside all These engineering areas can say What I'm saying is correct, and that is that when we say we are ready to our laboratories within the different courses, one of the most important is or at least when So we talked about electronics and other things in where we are we are using different components. One of the most It is important for us to know what it is. what he is doing, what is he doing What does that component do? sensor, what does that do? resistance, what does it do, well, different components. So this Mathematical modeling will also be included. depending on what the sensor does and We can also involve him different components much more advanced. In this case, I only... I'm showing how we can mathematically represent a basic behavior of a sensor, how We can include that model of what it's like that the signal works that we we get when we add noise and when we add a delay. So, let's do an example. So, well, yes, as I have told you I've been saying this right now, uh when we tell ourselves, "Yes, this It works mathematically like this and that's it equations remain there, so no, the The idea is that we at this moment we can apply mathematics to different components. In this case, I was telling them, don't just stay with that telemetry, the sensors They use it way over there in very... programs specialized, but we already saw in This whole journey through this theme that Sensors are used in almost everything, that if we turn on a light bulb, Well, there we are seeing a type of digital type sensor that if we We're going to take our blood pressure, because very The sensor is probably in there. all the examples we have spoken. So, we're going to... to do, let's say, we can name it as a practical stage. Mathematically Let's see how a sensor works ultrasonic, which is what we see here on the left side. Um, like I said, it's It's very important that we see exactly how the sensors work, because even if there are, let's say, different or many ultrasonic sensors, each It may vary in its functionality. So, let's say at this moment Let's see mathematically how An ultrasonic sensor operates in this specifically the HCC04 case. So, uh basically We have, uh, what is, uh, let's say, the main relationship, we have what is uh the main relationship, how is it that uh Let's say that sensor is taking my data. In this case, I had missed it. Okay, I'm going to basically explain how it is. that an ultrasonic sensor works. This What the sensor does is measure a distance using sound. What it does is send an ultrasonic wave. This is going to bounce off the object and return to the sensor. So, the sensor will measure the time it takes for that journey. We see then that the sensor does not measure directly, there are so many centimeters of from me to such an object, right? But We see that this sensor is doing a measurement by means of h of let's say of the time it takes to go and return. So, let's first model what It is the main relationship, which is the first equation we see. This the equation comes directly from what It is physics, where we know that the distance equals speed because of the time. In this case, then, the speed of sound, which is what it is that we are working on. But in this We're going to divide that case in two. By What is divided by two? because I told them that the sound goes and comes back, that is, hm goes to have that rebound effect. So, we say that the sound goes It may take some time, but actually covered twice the distance to to be able to reach isopet. That's what they I mean the rebound, right? We only need measure the distance between the sensor and the object, but the truth is what it does The sensor goes to the object and bounces back. that signal. Then we have what is the modeling this sensor, eh with the noise, That's what I was talking about, time uh in which, let's say, the sensor measures, no It's perfect. They actually exist different errors, noise in the environment, objects, it could be for example an irregular object that is not completely flat and that the sensor has Well, there are different disagreements there. And there can also be different ones, Let's say, changes in what is the speed of sound, even if they are very minimal. So, in this part We add what is the value of NT, which Well, we had seen it before, uh, that mistake is going to represent us. So, it's like we, say, measure with a stopwatch, but that stopwatch There will be a slight delay. So, There in that equation we're going to have in That delay is taken into account. And finally We represent and model what is the dynamic response of that sensor ultrasonic. So, this sensor Specifically, it will not deliver the specifically distance. The sensor It takes some time to make your process, in order to be able to emit the signal, in order to await the echo, which is therefore like that rebound and in order to process the result. So, that's why in We include the equation, then, like that, uh slight delay. as if, let's say, a The object moves quickly, then the The sensor can then remain as a A little behind, as if thinking about it a little, to put it more simply colloquial. That's why We also determined here, For example, we already modeled mathematically many of the sensor behaviors ultrasonic. So, when we suddenly at some point in life we are working with a sensor ultrasonic, because we're not going to say, "No, It's that he works and he measures me and I I put it in the code so that it would measure me, but we already know what math there is behind the behaviors, some of behaviors, because they can model more. So, as we saw in that example of ultrasonic sensor, measure a distance It's not simply about obtaining a value. In In reality, the sensor applies different physical principles, as we saw, by For example, the speed of sound, along with with different mathematical models that They are going to relate time to the distance. Furthermore, we know the measurement. It is not perfect; it can be affected by noise, due to interference. So, This also depends on the response of the sensor. This proves, it proves to us we who measure, although It seems very simple, because there are a whole mathematical and physical process quite comprehensive behind. That, as I was saying, doesn't only happen with This type of sensor occurs with all of them. the sensors that can be part of of a telemetry system. After We analyze what the operation is I'm from a sensor. Let's say these sensors are not based on, These sensors within a system are not They are based solely on devices physical, but we can understand them such as different mathematical models that They are represented physically, right? Suddenly electronically and that we allow, let's say, to represent the reality, but that will always be behind every sensor is mathematics. So, in this sense, telemetry it becomes that tool fundamental in modern engineering, already which will allow us to acquire the data reliable, that's why also We do the modeling, so we know from the mathematical foundations of each sensor that the data that we we are getting, So that sensor doesn't just capture information about the environment, but to through mathematics it will allow convert that information into that useful knowledge for us to know if Whether those measurements are accurate or not, if We can trust them or not. Okay, so I'll tell you a little bit about Matin NOA, about what she is doing our Matin NOVA team regarding telemetry technology or different uh let's say related technologies. As they As I mentioned at the beginning, a pillar fundamental that we have strengthened both at UNAT and in the seedbed is the development of different systems of advanced telemetry that can apply to different sectors strategic. As you can see in This recognition, we have, for example, the first project that we presented at the nursery meeting the Last year, we implemented a variable measurement system soil and data analysis in crops water catejas. So, in this case, This project isn't just a measurement, you know. Let's say isolated, but it's going to represent a complete architecture telemetry. In this case we achieved it which is real-time data capture real, where we use different types of sensors. We can see that in In this project we used sensors. In This is the case we have in this first image We have what is, let's say, a sensor of the presence of water on Earth. We also have a temperature sensor. and ambient humidity, a gas sensor. And on the other hand, within the same We also have a system that is a, let's say applied analytics. We transform this raw data. Already We know that each of these sensors is working mathematically by inside. We saw one sensor in particular. ultrasonic that we use in this another project that I'll tell you about in a moment he. Uh, but on the inside, let's just say we obtain different raw data from information within a project and the we process so that a person can analyze them. In this case we used TeamSpeak, where we see different diagrams, where we see the history of different variables and different widgets, uh let's say indicators for to be able to tell the person in a more Simply put, what is happening? with those measurements. We also have, uh within Matin NOVA we are developing, let's say, one of our students are developing a prototype device mitigation for the Rivers flooding. It is therefore an initial prototype where We see that the famous "eh eh" appears here. ultrasonic sensor that we already modeled mathematically how it works. So In this case, we have the measurement of river level that is made by means of the ultrasonic sensor. We already know the distance, the speed, let's say it goes It will be measured using that sensor ultrasonic, that level that river has to know if it's dangerous, if it's point of overflowing or if we can be Don't worry, we already know mathematically how does that sensor work and also We have what is then rain. Many times, let's say, in the... programming software, because we cannot simulate many sensors, but if we can simulate, let's say, different levels. So that's the prototype, or let's say the two prototypes or the two systems main ones that it is developing Matinova regarding what is the telemetry. Uh, finally, then, I would like Let them keep that lesson. that we can see at those sensors, to that telemetry, not only as systems that they are measuring, that they are obtaining data, but it is very important we understand mathematically by What's happening inside? So, to the Throughout this exhibition we saw how each measurement, let's even say something so Simply because there are many more sensors. complex, uh, how to calculate the distance with an ultrasonic sensor implies really the application of models mathematicians who are going to relate variables, they will consider errors, they will to describe, Let's say, how is that going to evolve? information that is being gathered in the time. That leads us to an idea very important, and that is that we the We cannot see mathematics only as theory, but as a tool It is essential that it be present in all engineering systems. So, from the most basic measurement even much more advanced technologies like those of us who live off NASA, from Apollo, from Artemis, eh, everything is built Based on these mathematical models, from very basic to probably much more complex. So, in this In that sense, telemetry is that clear example of something we have been told always, and that's because mathematics is in everything, as we saw throughout this Tomorrow, mathematics is involved. in many projects and in this case, well They allow us to transform that data into information and more than just information in useful knowledge. Finally, I want uh, to remind those who extend the invitation work, those who suddenly after This talk, or the talks we had in the morning, to those who are there, Let's say, uh, interested in what is the telemetry, data collection, to that they first see it as a pillar fundamental and that we don't see it as, I I know it's been very repetitive, but Let's never see devices as devices that work together, like that bad saying which, in my opinion, is a bad saying that if it works, don't do it Move it, won't you? Well, the idea of ​​one, let's say study and expand that knowledge It's about knowing that from the ground up why It's working. So, I reiterate the invitation to What do you think of our seedbed? What we're doing is interesting. the seedbed, so join us. I'm leaving you the contact information again for Our leader of the seedbed, Daniel Moran. In this case, as I told you, We have a very large team of teachers, students, both from Prado as postgraduate students, as graduates, that We are all committed to developing different proposals. In this case, Matinova, yes, it is something that is linked to education, to innovation, to virtualization of learning mathematics, but the truth is that within the seedbed we are not so rooted in that, but if you Do you have any projects you'd like to do? Well, how to bring it to the surface, h would be the opportunity to belong and so what can also take advantage of these opportunities within, let's say to belong to any of the seedbeds. But not only this, although It would be great if they participated in our seedbed. Uh, this, the truth It's a very important opportunity so that you all can develop. those investigative skills that if Do you have a project you want to Applying it to their territory, it's not that in where I live, where I live Something happens and I want to do such and such prototype. So, through these seedbeds, let's say it could be more Easy, uh, uh, let's say all these developments. So this is what