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# Circle Math

startsomething
So a circle is a regular polygon with infinate sides. For the longest time people didn't believe me. So I tried to prove it to them. And this is what I came up with:

A=pi * r^2
A=1/2 * a * p (a = apothem or the distance from the center to perpendicular to an edge , p = perimeter)

a is the same as r
p is the same as C (circumference)
C is pi * D
and D is 2r
so....

A=1/2 * r * pi * 2 * r
A=pi * r^2

cool huh?
now I just have to figure out what pi is... really.
I think because circles have infinate sides, pi goes on forever. So does this mean that there is a constant like pi for every regular polygon, that is not infinate? hmmm....

Whatcha think?
ml
another cool thing about circles (i figured it out myself)

for the caculation of the perimeter of a circle, you approximate the circle by n isosceles triangles from the center to circumference.

for the outer side of one trinagle you get:

outer side = 2 * sin((angle in the center)/2) * r

for n triangles you get:

perimeter = 2 * r * n * sin(180°/n)

then you go for the limit for n -> infinite

lim(n->inf) (2 * r * n * sin(180°/n)) = 2 * r * lim(n->inf) (n * sin(180°/n))

and guess what the last limit is! its PI

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