Date: May 29, 2013 11:07 AM
Author: RGVickson@shaw.ca
Subject: Re: Calculate angles, sides and areas for any regular polygon without<br> using trig functions and Pi
On Tuesday, May 28, 2013 5:35:58 PM UTC-7, JT wrote:

> Do you think i could calculate all the angles in turns and the lengths

>

> of sides(perimeter) and area of any regular polygon without using

>

> trigonometric functions and Pi?

Why don't you do some reading about what is known, and has been known for hundreds of years? You just cannot avoid irrational numbers when getting the sides, etc., of most regular polygons. That means that you can NEVER express the answer in terms of a nice fraction (i.e., rational number). If you claim to be able to do it you are provably doing something wrong, because it cannot be done. Period. End of story.

A nice, expository article that discusses some of the history (what the Greeks knew, what Gauss discovered, etc) is given in

http://www.math.iastate.edu/thesisarchive/MSM/EekhoffMSMSS07.pdf

This article has actual derivations and proofs of some of the formulas. Of course you can avoid calculating pi, just by expressing the angles in degrees instead of radians. The issue is how you can calculate trig functions of various angles, and that is what the various formulas are doing.