A couple of years ago, I came up with this formula: $$\lim_{n\to\infty}\frac{180\left(\pi^2r^2\cot\left(\frac{180}{n}\right)\right)}{n\pi}=\pi r^2$$
I derived it from a geometric perspective and just wanted to know whether it was anything knew or if there was something like this on the web. I also wanted to know how you would derive it from a calculus perspective and whether anyone can figure how it would have been derived as I have forgotten small potions of the derivation of the formula. As an addition if you could explain, I had my original formula and had to multiply it by 180/pi or one radians, explaining the 180 on the top and the pi on the bottom. Is there a reason why I had to multiply one radian?
Thanks!