ShmoopTube

00:04

Geometric Planes, a la Shmoop.

00:07

It's a bird!

00:08

It's a plane!

00:09

It's… Shmooperman!

00:11

Oh, wait. Our bad. It is a plane.

00:14

A geometric plane.

00:16

In geometry, planes are undefined notions, along with points and lines.

00:23

It just means that defining them is a bit tricky, but we can still describe them.

00:28

Planes have infinite length and infinite width, but no depth at all.

00:36

You can think of them as infinitely thin sheets of paper that extend forever in all directions….

00:42

…kind of like your mom's collection of wrapping paper around the holidays.

00:46

Of course, since we can't draw something that has infinite length and infinite width,

00:50

we settle for drawing something like this.

00:53

That's plane M.

00:55

Just like any two points define a line, any three points can define a plane.

01:01

That's the reason tripods don't wobble nearly as much as bipods do.

01:05

And that's also why bipods… don't really exist.

01:09

So given this figure, which points are NOT on plane M?

01:18

If a point is on a plane, we usually draw it within the boundaries of the plane.

01:22

These boundaries aren't real, of course, since planes go on forever.

01:25

But drawing those boundaries spares our brains from trying to visualize infinity.

01:30

The points that are on plane M are H, B, C, D, and F

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because they're all contained within the boundaries of M.

01:38

That means that the rest of the points… highlighted here for your viewing pleasure...

01:42

A, E, and G… are not on plane M.

01:46

Which points are both on planes M and N?

01:50

As in Mike and Nancy.

01:52

For points to be on both planes M and N,

01:56

they need to be contained within the boundaries of those planes in the figure.

02:02

We can see that points H, B, C, D, and F are on plane M,

02:05

and points A, B, C, and D are on plane N, Nancy.

02:09

Only points B, C, and D are shared by both those planes. And they're collinear!

02:20

Just like two lines intersect at a point, two planes intersect at a line.

02:24

Points B, C, and D are on the line that results from the intersection of planes M, Mike, and N, Nancy.

02:30

So… while a geometric plane isn’t going to swoop in and catch

02:34

you after falling from a 37-story window…

02:37

…it’s still pretty… super.

02:38

What were you doing that close to the window, anyway?

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