Circumference

Epicycle

Pi

Epicycle

I know how to calculate the area of a circle.

So what is the circumference?

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

Do it mathematically correct.

Of course not.

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

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

Select a point on the circle...

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.

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.

Circles around the Origin.

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.

Start transport from this point of the circle

What about bigger numbers?

Pi's just a number.

He's reciting the digits of pi.

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

Transport a measure on this circle

Select the segment to transport on the circle...

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

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

And it amazes me that this and it never repeats.

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.

Since Archimedes, people all over the world have been obsessed with calculating Pi.

It's safer to go around the lake.

Too much garbage in your face?

Even Newton and Leibnitz, who did a lot of calculus in the late 17th century, devised additional methods of calculating Pi.

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

We sat around the fire in a circle.

We sat around the fire in a circle.

What is the circumference of the circle?

Zhou Yu. Viceroy Zhou