Name: 数学の反則 - 点、線、面 (Math Antics - Points, Lines, & Planes)
Uploaded: 2021-01-14T06:24:03.000Z
Duration: 7 min 54 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

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Hi there! Today on Math Antics we're starting a new subject where we're going to learn the basics

of a special kind of math called Geometry.

Geometry is the study of things like lines, shapes, angles, distances and things like that.

In this video, we're going to focus on three of the most basic elements (or parts) of Geometry.

Alright, we're gonna start with points because they're about the simplest thing you can imagine in Geometry.

What's a point? Let me draw some for you.

But they do a really important job in Geometry...

They help us describe specific locations in space,

But they won't really help that much unless we name them

because if I say, "Hey look at that point over there!"

It's kind of hard to tell which one I'm talking about.

So what names should we give these points?

Well let's see… hmm… How about Archimedes,

How about Daphne and Einstein… let's see...

You know, on second thought, those names are kind of long and complicated.

Why don't we just use the first letters a each name instead?

"Look at point A" or "Look at point B", you know exactly what I'm talking about.

Let's just talk about 'point A' and 'point B' for a minute.

If you start at point A and go to point B, taking the shortest distance possible,

A line is the next most basic element of Geometry.

We name a line by the points that it goes through.

For example, we would call this 'line AB',

because its end-points (where it starts and stops) are points A and B

But, technically, this isn't really a 'line'… it's a 'line-segment'.

"What's the difference?" you ask. That's a good question.

A line-segment has a beginning and an end.

It starts at one point in space, and it ends at another.

A line, on the other hand, just keeps on going...

just like the number-line keeps on going forever.

Well, at least we imagine that it goes on forever.

We can actually draw a line that goes on forever, so here's what we do instead.

To draw a line instead of a line-segment,

you just go past the end points a little bit,

and you put an arrow on both ends of the line to show that keeps on going.

Now there's one more special type of line that we need to talk about,

and it's basically a combination of a line-segment and a line.

Rays have beginning points, but no ending points. They just keep on going forever...

but only in one direction.  So we only put an arrow on the end that keeps going.

In Geometry, each of these three types of lines

you can just write "AB" with a line over the top.

you can write "CD" with a double arrow line over them,  like this.

And finally, instead of writing "ray EF",

you can just write "EF",  with a single arrow line over them, like so.

And you know that you can  form a line between any two points.

The next thing we're gonna learn about is planes.

No!  Not the kind of planes that you fly in.

Now to help you understand  how planes in Geometry work,

Let's go back and look at all those points we had at the beginning of the video.

It looks like all the points are the same depth on your computer screen, right?

and if they were,  we'd say that they're all in the same 'plane'.

That's because your computer screen is a plane.

It's a flat surface like a window,  or sheet of paper, or a tabletop.

A plane (or flat surface) is what we call a two-dimensional object

because there's two dimensions that you can move in.

You can go up and down, or you can go left and right.

A line, on the other hand, is a one-dimensional object.

there's only one dimension that you can travel in.

Sure, you can go forwards or backwards along that line,

But if you're on a plane (a two-dimensional object),

All three of them are on that flat two-dimensional surface

Cool! So that means that if I want to get to point D,

I can do that too because it's on the same plane as A, B and C. Right?

Point D really isn't in the same plane as a computer screen.

It just looks like it from the position you're viewing it from.

Watch what happens if I start rotating the screen space a little bit.

Ah ha! Now you can see that the points are actually scattered all over the place in space.

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数学の反則 - 点、線、面 (Math Antics - Points, Lines, & Planes)

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