I'm not even sure that we all exist on the same plane of consciousness.

For example one problem with a quadrilateral is that the surface is poorly defined if all four points are not in the same plane.

And then up here would be the intersection of the plane and the top one.

When you use a mouse, your hand is down here on the mouse pad.

Please save us!

This is a vector field in 2 dimensional space.

Let's see if I can draw it decently.

But what if our world were two dimensional?

So it goes through point C and it goes through point D and it just keeps on going forever.

Plane

Plane

plane

The area of this figure in furgles square furgles, I should say the area is three square furgles.

isosurface

Iso Surface

Flat Map

So this is my three dimensional plane.

You'd show them something like this, wouldn't you?

But when you view it looking straight down onto it, you're

In particular, it could invent things like a curve which fills the plane.

I think you get the idea.

Now I'm going to challenge you. I'm going show you a video.

And they never intersect! They never intersect. So they're on the same plane but they never intersect each other.

She came to bespeak a monument for her first love, who had been killed by a whale in the Pacific ocean, no less than forty years ago.

I could have a plane that goes like this where that point A sits on that plane,

plane, like you can kind of view the projection of the surface of the xy plane, or the shadow of the surface of the xy plane.

I'm going to ask you a few questions about the state itself. So here's a quiz.

But I think you get the idea.

This is a plot of p of x, where the height above of this, where the height of this surface at a particular point, so given a particular x1 x2 values of x2 if x1 equals 2, x equal 2, that's this point.

Stand with one foot in front holding the other one 6 inches off the ground, parallel to the ground.

So if my plane looks like this I know it's very hard to read now and you wanted the intersection of this plane, this green plane and the cone I should probably redraw it all, but hopefully you're not getting overwhelmingly confused the intersection would look like this.

If I were to just flip this over like this, so we're

And on top of the coral reefs are sand banks.

These are graphs that can be drawn in the plane on a flat piece of paper so that the edges don't cross.

And then the base of it, the base I'll do in magenta will be this plane.

And if the two variables are positively correlated, then mostly likely if you're above average on one, you're above average on the other.

So what this does, it defines a vector that's associated with every point on x y plane.

Let me ask you a localization question.

So that's the plane.

Max. number of clipping planes

Problem 38.

Let me see if I can draw that.

It's this vector right there.

Shizuoka, one of Japan's prefectures, faces the Pacific Ocean.

And on top shelf is a turkey.