HMMMMMMM !! ![]()
I just looked at part e some more...
The formula for the "perimeter" of a circle is
c = 2 * r * pi
The formula for the perimeter of a n-gon is
p = 2 * r * sin(\(\frac{180^{\circ}}{n}\)) * n
With really big values of n , sin( \( \frac{180^{\circ}}{n} \) ) * n must be close to pi !!
So...I tried that
with n = 1,000: sin( \(\frac{180^{\circ}}{1000}\) ) * 1000 ≈ 3.141587
and
with n = 50,000: sin(\(\frac{180^{\circ}}{50,000}\) ) * 50,000 ≈ 3.14159265
I thought that the limit as n approaches infinity would make it exactly pi,
but WolframAlpha doesn't seem to say that.. here
But if I put pi instead of 180º , it works...? here