Math CentralQuandaries & Queries


Question from Levan:

This was the closest to what I am trying to solve.

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.


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