Chapter3 : Geometry

Hi everyone! Welcome to geometry! Today, we will be talking about points, lines, and planes! First, a point is an exact spot that represents a position, and it has no dimension, which means that it has no shape or size. We often use a dot to show a point. For the purpose of our exercises, we will use our foot, planted on one spot, to show a point. Next, a never-ending number of points come together, one after the other, like this: copy. What do we get? A line! In math, a line is made up of points and has one dimension. This means that it has length, which means that we can walk back and forth on a line, but has no width, which means we cannot go right or left, or depth, which means that there is no thickness—so we cannot jump up or down in a line.  Okay, now imagine that a never-ending number of lines come together, like this: copy. What do we get?  A plane! A plane is a flat surface that has two dimensions, which means that it has both a length and a width, so we can walk back and forth, right and left, but no depth, so we still cannot jump up or down.

Hi everyone! Today, we will be talking about dimensions. In the last video, we mentioned that a dot has none, or zero dimensions, which means that it has no shape or size. We can’t move at all! A line, on the other hand, has one dimension, which means that it only has length but no width nor depth, and a plane has two dimensions, which means that it has both length and width but still no depth. Okay, so what about three dimensions? Imagine that a never-ending—or infinite—number of planes come together. We say that spaces like this have three dimensions, which means that it has length, width, and depth. And this is the world we live in. Look around! Even your room has a length, a width, and a depth! We can walk back and forth, right and left, and also jump up and down in a room! Before you go, let’s try a quick example to better understand these dimensions. First, for zero dimensions, stand still with your feet planted on the ground, and imagine that you have no shape and no size, which means when the music turns on, you can’t move! Ready? go! Next, for one dimension, because it only has length and no width, you can only move back and forth when the music turns on. Ready?  go! You got it! Now, for two dimensions, because we now have both length and width, we can move around any way we want. We just can’t jump! Lastly, for three dimensions, we can use both the length, width, and the depth of the room, so we can move around, even jump, anywhere and everywhere we want. Ready, go!

Hi everyone! So in the last few videos, we learned that a plane, or a flat surface, has two dimensions, which means that it has both a length and a width. In the next few videos, we will be learning some of the basic two-dimensional shapes that we can make on a plane. First, to get the basic ideas of geometry, imagine that I have paint on the bottoms of my feet. (Move through the room with a curvy pathway). Did you see my pathway? What sort of paint marks did I make? Curvy lines! Like this, Dancers use pathways when they dance. Pathways are the trails we move through the dancing space. We can use curvy pathways, straight pathways, and zigzag pathways. Now, it’s your turn. Begin by skipping in a curvy pathway. Curvy pathways have no sharp corners and the lines are not straight. Imagine that you are painting curved lines through the dancing space. Now, try marching in a straight pathway. Use a sharp corner when you need to change directions. And remember, straight pathways have no curvy lines. Okay. Now, we’ll tiptoe with a zigzag pathway. Zigzag pathways have straight lines and sharp corners, but there are no curvy lines in a zigzag pathway. You got it!

Hi everyone! In the last video, we looked at three different pathways: curvy, straight, and zigzag. Now, we will use frozen body shapes and pathways to make dances about geometric shapes. The first shape we will learn is a circle, which looks like this. How many sides does it have? For two dimensional shapes, a side is a straight line, with no sharp turns, that make up the shape. But for a circle, there are no straight lines, so there are zero sides! Next, how many corners does it have? None! So a circle has no sides or corners. Instead, A circle is a shape made by a curvy pathway. Now, imagine that we have paint on the bottoms of our feet, and let’s skip in a circle pathway. Maybe you painted a big circle, or a really small circle. But if you are spinning in one place, you are not making a circle pathway; as we learned before, you are just making a dot! Pathways are a locomotor, which means that you are actively moving through the dancing space, not staying in one space.

Hi everyone! Today, we will be learning about triangles, which look like this. Can you tell how many sides a triangle has? One, two, three! It has three sides. How many corners does a triangle have? One, two, three! A triangle is a shape that has three straight sides and three sharp corners. In fact, to be a little clearer, a corner has two parts: a vertex and an angle. Let’s try walking in a corner. Here, a vertex is the point where we make a sharp turn. So right here, at this point, will be the vertex of our pathway. Next, an angle shows how much we turn. We could only turn a little, like this, or alot, like this. An angle has a number that shows us the amount we turn. So now, when we say that a triangle has three straight sides and three corners, we know that this means a trainle has three sides, three vertices, and three angles! To better understand this, let’s make a triangle with our body. Let’s tiptoe in our own triangle pathways, and make sure you have three straight sides and three sharp corners. Like this. Now try on your own!

Hi everyone! Today, we will be learning about another common two-dimensional shape: rectangles! Looking at the paper, can you tell how many sides a rectangle has? One, two, three, four! A rectangle has four straight sides. What about corners? One, two, three, four! A rectangle is a shape that has four straight sides and four corners, or, as we learned in the last video, four vertices and four angles. To better understand this, let’s make a rectangle with our body. March in our own rectangular pathways, and make sure you have four straight sides and four sharp corners. Like this. Now try on your own!

Hi everyone! In the last video, we talked about rectangles. Today, we are going to look at a type of rectangle, called a square! Can you tell why this is special? Well, it has four straight sides and four corners, so what can be so special? It’s because the four sides all have the same length! In fact, a square is a shape that has four straight sides that are exactly the same, four vertices, and four corners. To better understand this, let’s make a square with our body. Let’s march in our own square pathways, and make sure you travel the same amount of steps for the four sides. Like this. Now try on your own!

Hi everyone! In the last few videos, we explored some two dimensional shapes that are made on flat surfaces. Now, we will learn about three-dimensional shapes. These shapes are also called solid shapes, which means that they have a length, width, and depth. In the next few videos, we are going to model three-dimensional shapes with our bodies. But before we begin, understand that it is very difficult to make some of these shapes, so our task is to make our best representations of the shapes. Okay, so today, the first shape we will be looking at is a sphere. A sphere is a perfectly round three dimensional shape similar to a round ball you might play soccer or basketball with. And as you can see, it is made of one curved surface, kind of similar to how a circle was made of one curved line. One interesting thing to note about a sphere is that all points on the surface of a sphere are the same distance from the center. To better understand this, grab a friend and face each other while standing.  Then, stretch one arm and hold each other like this: The place where your two hands meet will be the center of our circle. Now, your other arm will create the top half of the sphere, like this, and your legs will create the bottom of your sphere, like this. Form here, you can move around, but your center should not move and your hands should not fall apart. Imagine you have paint on your legs and your bent arm. Then, the way you moved would be in the pathway of a sphere, because your bodies will always be the same distance from the center: the length of your arm!

Hi everyone! Today, we will be learning about cylinders! A cylinder is a three dimensional shape that looks like this:. Looking at this shape, can you tell me how many edges a cylinder has? Remember, an edge is a straight line, so there are no edges! A cylinder is only made of curvy pathways. And if it is only curvy, we also know there are no sharp turns, so there will be no corners either. So a cylinder has zero edges and zero corners, or vertices as we learned before. But what about faces? Well, can we find any flat two-dimensional shapes we learned before? Correct, there are circles! How many circles does it have? One, two! So a cylinder has zero edges, zero corners, and two faces. Let’s try modelling this shape with our bodies! Grab a partner, and together, make the top circle with your arms, like this: Now, we will be making the bottom circle. Imagine that you have paint on the bottoms of your feet, and walk around, together, in a circle while you keep the top circle in place. Like this: Now, you have a cylinder with two complete faces!