Select a point on the circle...

Start transport from this point of the circle

Circumference

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

Transport a measure on this circle

Select the segment to transport on the circle...

Epicycle

Pi

So what is the circumference?

Epicycle

I know how to calculate the area of a circle.

Of course not.

Do it mathematically correct.

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?

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

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

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.

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

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

OK, that's interesting.

Let's call it area surface.

Actually, never!

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.

Transport the measure of a segment or arc over a line or circle.

What about bigger numbers?

Pi's just a number.

He's reciting the digits of pi.

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

OK, this is a neat property of circles.

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.

Point A is not on the circle, point A is the center of the circle.

Or 2pi times the radius. 2pi times 4 cm which is equal to 8 pi cm. So this distance right over here is the circumference of either the top or the bottom of the cylinder.

Circles around the Origin.

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

We would call this JK, the two end points of the arc, the two points on the circle that are the inputs of the arc, and you would use a little notation like that, a little curve on top instead of a strait line.

So it's just going to be 3 times 2 or 3 plus 3, which is equal to 6 meters.

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.

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

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