# Circle

• May 11th 2008, 08:47 PM
Mathstud28
Circle
Here is somethign I am wrestling with conceptually because it should work theoretically I think but it does not

since $\displaystyle A_{\text{regular polygon}}=\frac{1}{4}n\cdot{b^2}\cdot\cot\bigg(\fr ac{\pi}{n}\bigg)$

Where n is number of sides and b is sidelength

Shouldnt $\displaystyle \lim_{n\to\infty}\lim_{b\to{0}}\frac{1}{4}n\cdot{b ^2}\cdot\cot\bigg(\frac{\pi}{n}\bigg)$
Describe a circle?
• May 11th 2008, 10:39 PM
CaptainBlack
Quote:

Originally Posted by Mathstud28
Here is somethign I am wrestling with conceptually because it should work theoretically I think but it does not

since $\displaystyle A_{\text{regular polygon}}=\frac{1}{4}n\cdot{b^2}\cdot\cot\bigg(\fr ac{\pi}{n}\bigg)$

Where n is number of sides and b is sidelength

Shouldnt $\displaystyle \lim_{n\to\infty}\lim_{b\to{0}}\frac{1}{4}n\cdot{b ^2}\cdot\cot\bigg(\frac{\pi}{n}\bigg)$
Describe a circle?

You don't have two limiting processes as $\displaystyle b$ is determined uniquely by $\displaystyle n$, for an $\displaystyle n$ sided regular polygon inscribed in the unit circle:

$\displaystyle b=2 \sin(\pi/n)$

RonL