So what is the circumference?

Circumference

Epicycle

Pi

Of course not.

Maybe it's 3 meters put some units in there.

So if you were to get your tape measure out and you were to measure around the circle like that, what's that distance?

Epicycle

I know how to calculate the area of a circle.

Do it mathematically correct.

Select a point on the circle...

And I were to tell you that its circumference is equal to 10 meters that's the circumference of the circle.

OK, that's interesting.

That's going to be the exact same thing as the circumference of either the top or the bottom of the cylinder

I can draw a neater circle than that. So let's say the circle loks something like that.

Actually, never!

Start transport from this point of the circle

And so for area we need to know the radius 'cause area's pi R squared, so we can figure out the radius from the circumference by saying, well circumference is equal to two times pi times the radius of the circle, or if you say 36 pi, which we were told this is the circumference, is equal to two times pi times the radius.

What about bigger numbers?

Transport a measure on this circle

It'll be the circumference of this ring times it's height.

And let's say when their tape measures weren't so good,

Let's call it area surface.

My volume is going to be 4 3...And then I don't want to just put a pi there because that might interprit it as 4 divided by 3 pi.

OK, this is a neat property of circles.

Pi's just a number.

He's reciting the digits of pi.

Then they find out that the diameter is roughly 2 centimeters.

Circles around the Origin.

Select the segment to transport on the circle...

In this painting that I made of the first 20 decimals of Pi,

If we do it with radians, we know that each revolution is 2 pi radians

It's that x point that we're evaluating it at.

With that out of the way, let's just apply this radius being 7 centimeters to this formular right over here.

So we're going to have a volume is equal to 4 thirds pi 7. cm 3.

I'm obviously passionate about the number and what we can do with it.

The circumference of this circle right over here which is the same thing as the circumference of that circle over there.

So how many meters do we have per revolution?

And remember that dimension is essentially how far did we go around the cylinder

And it amazes me that this and it never repeats.

A good man... draws a circle around himself and cares for those within.

And it's not just circles, either.

In fact, calculating Pi was used to test proper functioning of early computers.

(Laughter)

So we're worried about the ratio let me write it like this.