And for him, it wasn't so much the way the music goes as about what it witnesses and where it can take you.

And let's say I have some surface.

So if I were to draw the top view.

Let me see if I can draw it.

Click to draw dots or drag to draw strokes.

Let's visualize just what 8 plus 3 is.

It would look something like, let me draw the uh whoops.

And we've done this many times before.

So let's draw those two lines.

looks like just yet.

So that's my ellipse.

This could be interesting.

The third is three times as long.

And there's this reference to Le Petit Prince where the narrator asks the prince to draw a sheep.

Draw cartoons

Circle Draw a circle

If b was larger than a, I would have a tall and skinny ellipse.

Let's find the volume of a few more solid figures, and if we have time we may be able to do more surface area problems.

So a hyperbola usually looks something like this.

looks just like that.

And then, the middle one was the mauve layer.

And the best way to do is to separately visualize each of the separate layers.

18 divided by 3 is 6, so you get 1 6.

You see that I'm beginning to really lose control here and also hope.

Let's talk about the problem of finding a path through a maze.

This is going to be my y axis.

Drag and Drop graph plotting

So let's do this.

Well, I'll just leave it right over there.

It's also the case if the beaker was thicker.

So lets do 15 plus 46. We will get a different color.

And let me draw an odd function for you.

The teacher was fascinated. She went over to her, and she said, What are you drawing?

Let me clear out all of these and I will just draw a solid line.

One cube has side length 2.

Ellipse Draw an ellipse

And then what does vector y look like?

You know we drew y.

Then it turns its heading into this direction over here, and this is π 8.

This is kind of the key intuition here.

And that is equal to dx no, sorry, this is dy.

And in fact, all of these things over here are rational numbers.

let's just think about what's going on.

Well, a square is just a special case where the length and the width are the same.

In order to understand this question and what we need to do,