posted on Aug, 4 2014 @ 12:18 PM
As I was playing with my calculator trying to find a direct relationship between the two mathmatical constants π (Pi) and φ (Phi) -- something
remarkable happened. I actually made it!!! Obviously, this is not the right forum for mathematics, but since there are no subforum here dedicated to
math, and since I'm always looking for a lady who would find stuff like this fascinating, here we go:
A few years ago, while fiddling with my pair of compasses and the usual straightedge, I discovered a way to design a perfect ten-pointed star. Being
quite sturdy in geometry, but not so good at arithmetics, I didn't seem to be able to actually prove it in a formula or equation. Constructing the
star, what I did was I divided the radius of a circle in the golden proportion and used this measure to plot a decagon (or a ten-sided polygon/star).
But how would I explain this with numbers and letters? That there was a direct relationship between Pi and Phi in a way I had never seen elsewhere?
Seeing π*φ equals roughly 5, I realised that the extra decimals would simply be there due to the fact that the circumference of a circle is slightly
longer than the perimeter of a decagon or a pentagon. And the perimeter of a polygon is given by:
==> 2nr sin(π/n) where n is the number of sides and r is the radius
Given my circle and decagon shared the diameter equaled to 1 (thus the circle has a circumference of π, since 2πr=c), I came up with the
==> 5 / (2*10*0.5 sin(π/10)) = φ = 1.618033989...
or in other words ==> 5 divided by the perimeter of a decagon with diameter 10 equals the golden number Phi precisely. Now. Does anyone else find
stuff like this eh, what's the word-- sexy?
I think I deserve at least a lesser goddess for this discovery....
edit on 4-8-2014 by Utnapisjtim because: woohoo