Universal Theory via Euclid's Method

Hello everyone,

So in past days, I gotten involved in some research on linguistics and etymology. As a computer scientist, I was lucky to draw parallels between a "human" language vs. computer languages.

Also, I came across Euclid who actually constructed the Geometry we use today. He did so through his own method. Euclid's method.

Anyway, I am publishing my results in a concise form here. Although, the thing is a bit challenging I hope it will drive some interest.

utem


"Literated in English and Turkish"

Anyone who sees this understands the meaning of one
Anyone who sees this is someone that understands

Bunu gören biri anlar


The literal meaning of the diagram is actually intriguing...

Best regards,
elasolova

Guess I didn't see it...

Ok. Assume a circle with radius 1.
Denote its area A.
A= pi * r^2
Since radius is 1.
A = pi

Assume we have a partition of this object with golden ratio, partition is centered at the origin.

Thus, 2*(a+b) = pi

Where, a is the bigger partition and b is the smaller and a/b = y , where y is the golden ratio.



namely (a+b)/a = a/b, meaning that (a+b) = (a^2)/b


Now substitute 2*(a^2)/b = pi

2*(a*a/b)=pi

a is the bigger partition generated with golden ratio partition. Thus, a=y*A (meaning that whole area A times the golden ratio gives a).

a/b is glden ratio itself.

thus 2*(y^2*A) = pi,

2*(y^2*pi) = pi (assuming radius is 1)

2*(y^2) = 1 (contradiction)


What this proves is golden ratio is a more general thing than pi ratio

A = a+b, so not 2*(a+b)=pi but a+b=pi. Also, if a is the bigger partition, then a = A/y, not a=y*A. Doing your calculation with those corrections results in A=pi, which we started with.

Yeah, sorry. I got carried away I guess. But I still suspect that golden ratio is more general than pi ratio.

Why? And what specifically does "more general" mean?

Ok. So pi can be written in terms of golden ratio this is what I mean.
y = golden ratio

y = 2cos(pi/5) - not my own proof but I am almost sure it is correct as it is also listed in wolfram alpha, http://www.wolframalpha.com/input/?i=golden+ratio

thus, pi = 5*cos^-1(y/2) , pi = 5*cos^-1((1+sqrt(5))/4), which is an exact closed form of pi, http://www.wolframalpha.com/input/?i=5*cos%5E-1%28%281%2Bsqrt%285%29%29%2F4%29


I mean idk. People write golden ratio in terms of pi. But, writing pi in terms of golden ratio will (perhaps) be more productive as golden ratio has a simple closed form expression.

Then why not cos^-1(-1) for pi? Or perhaps nicer is ln(-1)/i, as you might consider ln more general than cos?

What exactly becomes more productive when using such a closed form?