On 29 Maj, 17:07, Ray Vickson <RGVick...@shaw.ca> wrote: > 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.
I do intend to use radians nor degrees, i will use turns, ratios and triangles to solve it for any polygon and the forumula will be expressed as a ratio vs the vertex line. So the vertex line will be one and the vertices ratios of one.