Golden Ratios from the Diagonals and Sides of
		Regular Polygons with Odd Number of Sides
		Also, a selection of Polygons of Fermat-Prime
		Number of Sides

Note:
^ is symbolizing exponentiation, the raising of a number to a power.
<> are brackets surrounding the square root of an expression.

TotAng is short for ==> Total of All Internal Angles Along each Polygon's Circumference
3-Gon is an Equilateral Triangle, 5-Gon is a Regular Pentagon, etc.....
??-prime is one of the five Fermat Primes: 3, 5, 17, 257, and 65,537, 
	which are the first five terms of the Fermat series, derived by the formula 
	2^(2^n) + 1 = 3, 5, 17, 257, 65'536, 4'294'967'297, etc....
n is the simple integer progression, of: 0, 1, 2, 3, 4, 5, 6, 7, etc....
The Greek letter "Phi" is often used to designate "golden" ratios.
Each of the roots generated by these fermat programs are golden ratios within their 
"polynomial set".

From the sixth term (where n = 6), and upwards to the infinith term, all successive 
Fermat numbers may be composite. Polygons composed of composite Fermat Numbers are 
unconstructible using only straight-edge and compass. See here for more on this:
http://vinyasi.mayashastra.org/References/Mathematics/Fermat_Number.html#constructible
Consequently, any polynomials which are generated from the golden roots of unconstructible 
polygons will be unsolvable. Polynomials (in one unknown, x) that are solvable yield solutions 
for x of the form: x = some formula of numbers, such as the quadratic roots of the 5-Gon: 
x = (-1 ± <5>) / 2. We could still generate an approximation of roots from the infinite class of 
unconstructible polygons of odd number of sides using trigonometry similar to what is being done 
within these two files:

fermat_executed_from_command_line
Use this file if you have access to perl from a terminal window, such as a DOS window on your
pc that has perl installed, or else (dial-in?) access to a shell account with a remote computer 
that hosts perl (mostly likely). It will create a file: html.txt that will have some data in
html (web-ready) format.

fermat_executed_from_browser_window.html
Use this file if you have perl installed on your pc and want to test the program using your 
browser without creating a data file. This will work if your pc has 'PerlScript' and ActiveX 
installed. An alternative is to deliver the data to (internet or intranet) clients with the help 
of a server. See below for more information:

ActivePerl
http://www.activestate.com/Products/ActivePerl/

PerlScript - ActiveX scripting engine, like JavaScript or VBScript with a Perl brain.
http://www.activestate.com/Products/ActivePerl/system_requirements.plex
http://aspn.activestate.com/ASPN/Reference/Products/ActivePerl/Components/Windows/PerlScript.html

Help with using Windows Scripting Host
http://aspn.activestate.com/ASPN/Reference/Products/ActivePerl/Windows/WindowsScriptHost.html

The Phi-roots that are generated by these programs can be approximated using many different 
methods. Two methods are possible using the information gleaned from the resulting data. One way 
is by using triangles (what I sometimes like to refer to as: "wedges") within regular polygons 
of odd numbers of sides. Each polygon is oriented with one of its sides along our visual-bottom 
putting one of its angles at its top. All of the triangles would then share their apex angle 
(the angle at their top) at the top of their surrounding polygon. Their bases would be shared 
along the polygon's base and along diagonals that horizontally cut across their associated 
polygon. The length of the base of each triangle is divided by the length of its slope. This 
makes each triangle's base equivalent to the Phi proportional value for that triangle while its 
slope is equal to the value of 1. Another way is to use trigonometry's sine function on one-half 
of each triangle's apex angle within this formula:

Phi is equal to the (sine of (PI * Apex_Angle / 360)) * 2

Additionally, every other result must be signed negative or else its resulting polynomial 
won't have integer coefficients.