Wednesday, May 10, 2006

Phi...the divine proportion, golden ratio, golden section, goldean mean, Fibonacci series, whatever you want to call it.

So I am reading The Davinci Code and came across this interesting concept. The number 1.618. Apparently scholars throughout time have came to an agreement that the number 1.618 is a divine number for several reasons. While doing my bachelors I took this course "Nonlinear Optimization". It mentioned this number Phi and how it can be used.
Phi is calculated by solving

for "x" and after many iterations it converges to 1.618. So anyway back to the point, why it so interesting? Some of these reasons you may be able to test out for yourself.

First a little history. Why was the Greek letter Phi chosen? It was first closely studied by a Greek scultptor called Phidias and as a result was given the name Phi.

Throughout time this number was used for many purposed. It seems like it envokes a certain emotion within humans. A lot of artists use this number in their designs and paintaings. Whenever balance is an issue, somehow the number 1.618 was the balance in any art.

So why was it said to be divine?
1. After reading this, I tried it out and surprisingly it came within .018 of 1.618 - probably due to measurement error.
The Golden Section, also known as Phi, is manifested in the structure of the human body. If the length of the hand has the value of 1, for instance, then the combined length of hand + forearm has the approximate value of Phi. Similarly the proportion of upper arm to hand + forearm is in the same ratio of 1: Phi . Coincidence?

2- Also if you measure your height, and then measure the height between your belly button and your feet, the ratio is 1:Phi again.

3- Several other examples were mentioned, the ratio of the radius of spirals to each in a seashell is 1:Phi, the ratio of distances between leaves on a twig is 1:Phi.

4- In university, or highschool if you ever came across the Fibonacci numbers, you were probably introduced to them as the quantities of rabbits reproducing:
So starting with 2 rabbits, they reproduce, now you have 3, more reproduction, now you got 5, and so on...
Well apparently this is not just an academic exercise, a lot of plants, organisms, creatures reproduce or produce new quantities at this rate. Coincidence?

5-Even the UN Building they say exhibits this phenomenon.

Since it all started with "x^2-x-1=0" I think it is all just a mathematical trick within solving that equation. Something to do with the "1" since that means "x^2-x=1",1 as in a whole. If you figure out the trick then please comment and let me know!

Baffled Nael Signing Out

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