Monday, May 21, 2012

The Golden Mean

Five Twenty One Twelve Spiral, copr 2012

Phi, 1.618, the golden mean, the, the golden ratio, the Fibonacci sequence and Fibonacci spiral,  all these are expressions of the same thing. The ancient Greeks used this math to portray perfection in art and architecture, having noticed that it appears again and again in nature from the tiniest seashells to galaxies. Ok I made up the galaxies. But they do follow the Fibonacci spiral.   One only has to look at one's own hand to see the application of the Golden mean proportions in the bone lengths of the fingers.  Waves at the beach follow this exact spiral shape, as do pineapples, sunflower seed heads, pine cones and every other form of life..

The Greeks were way ahead of their time however, because Fibonacci (aka Leonardo of Pisa) didn't show up until 1202 AD.  He talked about rabbit breeding in his book, Liber Abaci.  Must have been one of those one-off  sort of artist books because the printing press didn't show up for yet another 400 years.  I think he shows up in the fifties reincarnated as a piano player.  Anyway his imaginary rabbits reproduced at he rate of the Fibonacci sequence as explained here under Origins.  What all this has to do with this post I can't say.  But I wonder what was really on his mind.  Rabbits?  

I was drawn to the form itself, and how downright majestic it is.  However this spiral is not exactly a pure spiral, it's just a series of quarter circles drawn with one leg of a square as the radius following the Fibonacci pattern of squares and golden rectangles.   A true spiral would be drawn with French curves, a continuously expanding curve.  But who am I to argue with God.  I'm just one of the creeping things.



Franco said...

Beautiful work!!

Katherine van Schoonhoven said...

You find such interesting videos to share! The nautilus spiral is the logo for the Salvadore Dali Museum gifts (in St. Petersburg, FL). Did you want a tee shirt, hat, tote bag, or coffee mug with that image on it?

William Cook said...

Thanks so much Franco!

Hi Katherine--Thanks for the info on The Dali stuff. That would be a very cool shirt.

L.W.Roth, said...

This is beautiful Bill. You are such a complex guy. A deep thinker, I think. Your hand on the pen is very gifted.

William Cook said...

Linda--Thank you so much for checking in on this one--I was beginning to hear crickets. By the way, the Four Seasons are really at home on that tomato colored wall. Sharp! Best.

m.gaudreau said...

I have always loved the spiral. The celts invented it,you know, but only for fun. Wonderful work, Bill