Irrational Beauty

Posted by Ange

February 4, 2009

: Blue Flowers

: Sunflower and Bee

: Tulip

I am constantly amazed by the complex order of nature.

Take trees for example. You look at most of them and they’re pretty random, right?

Wrong!

The branches on many trees diverge according to a proportion known as the ‘Golden Mean’ or PHI (pronounced ‘fie’) which is 1 to (1+5^(1/2))/2) or 1 to 1.6180339887… That is, a little under two thirds of the way up a branch, another branch will begin.

Directly related to the Golden Mean is the Fibonacci sequence (1,1,2,3,5,8,13…) which has a closed mathematical formula based on PHI. The next number in the Fibonacci sequence can be found by adding the last two. For example, the next number in the sequence above is 21 because 8+13=21. This ratio appears consistently in nature in the form of spiral growth patterns (e.g. nautalis shell, leaves around a stem), petal numbers and arrangements, and even human proportions (think of the ratio of the length of your arm from elbow to fingertip compared to the length of your arm from elbow to wrist). That great DaVinci ‘Vitruvian Man’ picture was carefully composed according to PHI.

I think it’s great that some of the things we as humans find most beautiful on a primal level are carefully, naturally, and beautifully ordered. Truly Divine!

PS, If you’re interested, there is a neat book called Divine Proportion: Phi In Art, Nature, and Science by Priya Hemenway that gives a really great overview of the Divine Proportion throughout history, in nature, in science, in mathematics, and art.