Divine Proportion!


When we look at the bud of a rose, we see a striking thing. At the center of the rose is the apex, and around the apex the rose`s petals emerge, moving away in a circular order. Following their order of appearance, a generative spiral emerges and if we measure the angles between successive petals we find that to be 137.5 degrees.That is the Golden angle and is found by multiplying 360 degrees by phi, the ratio formed by successive Fibonacci Numbers.

Comments

Sid said…
Hi,
Interesting information there.

Although I don't know what is the angle between successive petals of a rose, the golden angle is actually found by:

360 (1 - 1/phi)

And also that the golden ratio is the limit of the ratios (and not the ratio) of successive terms of the Fibonacci sequence.
Koushik said…
Thanks for your comment. Phi=1.6180339...., so obviously your expression for golden angle matches the value 137.5 degree. When I was trying to find the mathematical relationship between nature`s symmetry and science, I came across a book "Divine Proportion: phi in art,science and nature" by Priya Hemenway. I think the author oversimplified things.
Anyways this mathematical description is applicable for pineapple, sunflower.
I can provide more information if you need it.