   SEARCH HOME Math Central Quandaries & Queries  Question from Levan: This was the closest to what I am trying to solve. http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/dj1.html So in the answer linked, we figure out what is "c". But what if we know "c" and want to find out "n" based on specific "r=1". It might be simple math, but I have not had any relationship with math for 20 years now but this question puzzles me for a reason. Hi Levan,

I am unclear as to what you want to do. It looks to me that you want to inscribe a regular polygon with side length $c$ into a circle of radius $r$ and your problem is to determine the number of sides, $n$ of the resulting polygon. On our page that you quote Stephen developed the expression

$c^2 = r^2 \left( 2 - 2 \cos \left( \frac{360^o}{n}\right) \right)$

which he then solved for $c.$ You want to solve this expression for $n.$

Is this what you want? The difficulty I am having is that for $n$ to be a whole number only certain values of $c$ and $r$ are possible.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.