Thursday, September 14, 2006

Woman on phone, Fibonacci, starlings

I pass a picture window close to the road, where a woman is sitting with a telephone and a cup of tea. Absorbed with the phone, she massages one bare foot with the other.

I have always been intrigued by the sequence of numbers discovered by the thirteenth century mathemetician Leonardo Fibonacci. In the Fibonacci sequence of whole numbers each number is equal to the sum of the preceeding two. Hence Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13 and on and on for ever. I have known for some time that the number of flower petals or seeds in flowers from the daisy to the sun flower, are nearly always Fibonacci numbers. Today, I read that, particularly as the numbers get larger, the ratio of each number to the preceding one "converges" on the number 1.618... which is the "divine proportion" or "golden mean"recognised by Pythagoras as a symbol of health and used by Euclid to construct a regular pentagon and other more complex figures. The ratio was apparently known to the ancient Eygyptians who used it in the pyramid at Gizeh where the ratio of the altitude of a face to half the side of the base is almost exactly 1.618. Renaissance artists among others applied the ratio in architecture and the composition of paintings, a fact that did not escape the author of the De Vinci Code.

On the cross bars of a telegraph pole sit rows of starlings like musical notes.

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