And you thought that the Golden Ratio was just a number..

[Mike_E]

As it turns out it's pretty basic after all.

Golden ratio discovered in quantum world: Hidden symmetry observed for the first time in solid state matter

 

[c.cloudwalker]

One major problem with this article. The golden ratio is not famous from "art and architecture." It is famous from nature and that is the main point of it.

 

[KmH]

Two of my favorite math subjects!

This is a very common misunderstanding.
http://en.wikipedia.org/wiki/Fibonacci_numbers#cite_note-40
The Golden Ratio, also known as Phi (1.6180339887), and the Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144..., where the next number in the sequence is the sum of the two preceeding numbers, are often confused because the ration of the two preceeding Fibonacci sequence numbers closely, but not quite, approximates Phi, the further into the Fibonacci Sequence you get.

It is the Fibonacci Sequence (named after Leonardo of Pisa, "son of Bonaccio") that is repeatedly found in nature, and not the Golden Ratio, which came to fame in art and architecture.

The Fibonacci Sequence was discovered by ancient Indian mathematicians but was introduced to western mathematicians by Fibonacci in 1202.

An excerpt from Wikipedia.org "Fibonacci Numbers":

Fibonacci numbers in nature


Sunflower head displaying florets in spirals of 34 and 55 around the outside


Fibonacci sequences appear in biological settings,[38] in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple,[39] the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.[40] In addition, numerous poorly substantiated claims of Fibonacci numbers or golden sections in nature are found in popular sources, e.g. relating to the breeding of rabbits, the spirals of shells, and the curve of waves[citation needed]. The Fibonacci numbers are also found in the family tree of honeybees.[41]

 

[Torus34]

Certain numbers have a habit of popping up in unexpected places. Base e and our old friend pi are two more of that ilk.

 

[c.cloudwalker]

The Golden Ratio is also known as the Divine Proportion, meaning it comes from God (the Gods) and is found in nature. Euclid's work, as that of many others, was an effort to unveil the mysteries of the universe and describe them through numbers as he did with the Divine Proportion but there is very strong evidence that it was recognized and used before.

Saying that it doesn't come from nature (the divine world) goes against every book I have read on the subject. For anyone interested, the one I liked best and own is "Divine Proportion" by Priya Hemenway.