Those of you to whom I have spoken of this know why I'd be explaining my interest in the beauty of the fibonacci sequence, the golden ratio, and phi.

THE MATH (skip if you get it)

Fibonacci sequence: After starting with 0 and 1, every number is the sum of the two previous numbers.

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 etc

After just 14 times that we have added each number to the one before it, the ratio between them stabilizes to a constant 1 to 1.61803399 (phi φ).

And that is the Golden Ratio. It is usually mathematically simplified as 1 : 1.61803. It is graphically simplified into the cleanest form of itself in a nautilus spiral.

If you graph numbers on an even x and y scale and draw a line from 0 to where 13 meets 8, the line's gradient is exactly 1.61803. The closest cross sections to that line will all be fibonacci sequence numbers.

IT'S EVERYWHERE

The Golden ratio is in human proportions, and in literally everything that grows because it is the perfect model of efficiency.

Well, Phi (φ) is important to me for the better understanding of beauty in the universe that I can gather from it. I like spirals. I don't worship them, nor do I see a greater significance on the grand scale than actually exists. But I do like to recognize them when I see them at work.

Every creature and every natural process and many "unnatural" natural processes like the building of crystals, the sworling of galaxies, and the rate of decay and new stars forming on the arms of those galaxies, the inner curl of a moving wave includes that golden spiral. So do the tiny bits of atoms that fly off into nothingness when you put them in an atom smasher. It is the mathematical representation behind nearly all the kinesis, efficiency and change that occurs in living creatures and even unalive but energy-filled matter alike. It may just come down to the rate of resistance of energy, both living and 'dead' against matter. I don't know, but in all things that grow, you find that ratio in nearly every measurement. My arm bones to each finger bone each is a perfect golden ratio. Even my fingerprint sworls include a perfect golden ratio.

DNA includes the golden ratio.

Once we discover the exact mathematical origins of the universe we live in, I will bet you it contains φ. Come on, bet you five bucks.

WHAT MAKES IT TREMENDOUS

Art contains the golden ratio, as do so many sciences.

It is the perfect model of grace. Everything approaches a perfection of grace and aesthetic as it gets closer to the golden ratio, as seen through the eyes of majority of the beholders out there. The better communicating artworks, the truly inspirational architecture, all contains the golden ratio.

Galileo, who effectively began the process that ended the dark ages for good, said:

Mathematics is the alphabet in which God wrote the universe.

He was trying very hard to convince Rome that his work in the Sciences was merely a further proof of the miraculousness of the world around us. Bacon, Galileo, Da Vinci. These men practiced sciences when there was a very fine line between scientist and heretic. Their brave curiosity and exploration in the face of death exalts us as a race, I believe, and is among the evidences in my answer to any debate over the difference between man and animal.

But we know that the ancients also were far greater than just animals. They knew this sequence, which - in order to be reached and grasped, assumes a pretty good understanding of sciences and math. Ancient cultures included its measurements into architecture, art and writings, long before Fibonacci. Which means it was rediscovered newly when Fibonacci named it. And that it is not merely a complication of mathematics. It is a rendering of the real world into a math concept. NO matter how many dark ages we reach, math survives. Which is refreshing and lovely.

Here is a simple TV show, Numb3rs, describing the golden ratio and the Fibonacci sequence:

Anyway, the point is, I am an artist. I am a geek. I am a history buff. I think that the Golden Ratio as an emblem is the perfect blending of all these things.

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Love it!

I'm a bit of a phi fan, too. What little Second Life modelling I do has a tendancy to end up with the golden ratio hidden in it somewhere! Have you read Livio's book on the subject? He does a fair amount of myth-busting about it, but has a real appreciation for the number's quality and prevalence in the natural world.

Oh, and what is awesome about the fibonacci sequence is that you don't have to start with a 0 and a 1. Any two numbers will tend towards phi if you run them through the same process. What I love about running fib numbers is the way the approximations of phi "wobble" around phi's true value. It's an irrational number, so we'll never get to the end of it, but that wobble is like a seduction to keep on looking; the dance of the infinite veils!

Julie will have to read this. She LOVES Numbers and has watched the episode about the Fibonnaci series about 12 million times.

Woah. I'm way too tired to actually read this. But wanted to comment, because I'm RAD like that.

You might like this T-shirt. It's the symbol Phi, made from the numbers in Phi. http://www.thinkgeek.com/tshirts-apparel/unisex/sciencemath/9eec/

I recently checked up on the mathematical origin of the universe. It doesn't contain phi, but it leads directly into the Fibonacci sequence and thus phi/the golden ratio flows from it. Can we split the $5 and call it even? :-)