Das Video kommt von YouTube: erst beim Abspielen verbindet sich die Seite mit YouTube (Google).
Math Antics - Polygons
Das Wichtigste aus dem Video
Tipp auf eine Zeit – das Video springt genau dorthin.
Transkriptautomatisch erstellt · 50 Zeilen
- Hi there, welcome to Math Antics! So far, in our series on geometry, we've learned about points, lines, planes and angles.
- In this lesson, we're going to learn about another important element of geometry. We're going to learn about polygons.
- You probably already know a lot about polygons because you see them all the time. Here's some common examples that you might recognize.
- These shapes are all polygons. That's because a polygon just means a multi-sided shape, and these shapes all have multiple sides.
- Okay, so that's a basic definition of a polygon, but to really understand what is a polygon and what is NOT a polygon,
- we need to learn about the specific properties that all polygons have in common. First we need to know the three parts that make up all polygons.
- And these parts are: sides, vertices, and angles. The sides are just the straight line segments that make up a polygon.
- And the vertices are points where the sides intersect. And the angles are formed by the intersecting lines.
- In fact, in Greek, the word polygon literally means "many-angles." So all polygons have sides, vertices and angles.
- This polygon here has 5 sides, 5 vertices and it forms 5 angles. The next thing we need to know about polygons is that they're 'closed' shapes.
- Now what does it mean for a shape to be closed you ask? Well, it means that the sides are connected so that there are no gaps.
- The area inside the shape is separated from the area outside the shape, and there's no way to get from the inside to the outside without crossing a line.
- It might help to think of a closed shape like a cage. If you put an ant inside the cage, there's no way for it to get out without crossing a line.
- But if the shape is open, then there is a way out. So these are all examples of closed shapes, and these are all examples of open shapes.
- And the important thing to remember is that a polygon must be closed. And the last thing we need to know about polygons is that they're 2 dimensional, or flat shapes.
- And that means that all the vertices must lie on the same plane. If any one of the vertices were to move forwards or backwards,
- so that it wasn't in the same plane as all the other vertices, then it wouldn't be a flat shape anymore. Flat shapes are also called planar shapes because all of their points are on the same plane.
- And even though polygons themselves can't be 3D shapes, you can use polygons to make 3D shapes. Like a box, for example.
- The box is not a polygon. But each of it's flat sides is a polygon.
- Alright then. We now have a specific definition of a polygon. A polygon is a multi-sided shape that has sides, vertices and angles.
- A polygon is a closed shape, and a polygon is a 2 dimensional, or flat shape. And now that you know that, it's time to play "Polygon or NOT a Polygon!"
- Now here's your host: me! Thank you, thank you! Alright. Now the rules of the game are simple.
- I'm gonna show you a shape, and you tell me if it's a shape, and you tell me if it's a polygon or not a polygon. Are you ready to play?
- Our first shape is a square! Is a square a polygon? Yes! A square has 4 sides and 4 vertices and it's a closed, 2D shape.
- So it is a polygon. And next we have, hmmm. I'm not exactly sure what to call this, but, is it a polygon?
- Nope! It's close, but because it's an open shape, it can't be a polygon. Alright, what about this one? Polygon or not a polygon?
- Yep! It is a polygon. Even though the sides are not all the same length, it is a closed, 2D, multi-sided shape. In fact, if you count, you'll see it has 7 sides.
- Ah, how about this one? Is a circle a polygon? Well, it is a closed, 2D shape, but how many sides does it have?
- Now that's the problem. A circle doesn't have any straight sides, vertices or angles.
- It's a curved shape, so it's not a polygon. Next we have a star shape, just like me! Is this a polygon?
- Yup! It has straight sides and vertices, and it's a closed, 2D shape. That means it's a polygon!
- And what about this one? Right you are, this is not a polygon! It's a dog! Ahh, here's an interesting one.
- It's a closed, 2D shape that does have straight sides andvertices, but, it also has this curved part here.
- Can it still be a polygon with that curve there? No! The curved part disqualifies it as a polygon.
- A polygon has to have only straight sides, so this is not a polygon. And what about this guy here? Is this a polygon? Well, it is just straight lines,
- but two of those lines cross, and if any lines cross it can't be a polygon. Plus, he has this big open end here. So this guy is definitely not a polygon.
- And last of all, what about this one? Right you are, this is not a polygon because it's a 3D shape.
- It's made from polygons, but the whole shape is not a polygon itself. Well, that's all the time we have for this week.
- Join us next week as we decide: "Is it Bigger than One?" Okay, so after playing that game, you have a really good idea of what a polygon is, and what it is not.
- The last thing I want to mention is that some polygons have special names depending on how many sides they have. Here's a list of the most important ones to know:
- 3-sided polygons are called triangles. Triangle are so important in geometry, that they'll get a whole video of their own.
- 4-sided polygons are called quadrilaterals. Wow! Now that's a fancy math word!
- But it helps if you just remember that the first part, "quad," means "4." Quadrilaterals are shapes like squares, rectangles, and parallelograms.
- They'll also get a video of their own. 5-sided polygons are called pentagons.
- 6-sided polygons are called hexagons. And 8-sided polygons are called octagons.
- By the way, polygons that have 5, 6, 8, or however many sides like this, are called regular polygons if all of their angles are equal,
- and irregular polygons if their angles are not equal. Of course, there are a lot more polygons than that, but you probably won't need to know their names.
- As long as you know what polygons are, and how to identify them, then you're ready to move on. The exercises for this section are pretty easy, so no excuses!
- Good luck! Thanks for watching Math Antics, and I'll see ya next time.
- Learn more at mathantics.com