
THE GOLDEN RATIO
The golden ratio is a pattern of order used by nature. We can see this pattern in the growth of the branches of trees, the seeds of sunflowers, and the leaves of plants, just to name a few examples. Thanks to this pattern, branches, leaves, and seeds receive the same amount of sun exposure and rainwater, since they do not block each other out. The golden ratio is also present in the structure of DNA, the bones of the finger, the proportion between the bones of the arm, forearm and hand, and the inner ear and outer ear, just to name a few, although science has not yet discovered the exact efficiency of the proportion in the human body.
Mathematicians such as Pythagoras, Euclid, Luca Pacioli and Leonardo of Pisa (Fibonacci); artists such as Botticelli, Michelangelo, Leonardo da Vinci, Dürer, Cézanne, Mondrian and Dalí; and architects such as Gaudí, Le Corbusier, etc. have utilized and revealed the uniqueness of the golden ratio as an expression of beauty, harmony and efficiency.
Nature & Numbers
A spectacular video about the omnipresent golden ratio in nature.
Fibonacci Sequence in Nature
This is a video compilation of clips from various video sources about the Fibonacci Sequence (golden ratio).
The magic of Fibonacci numbers | Arthur Benjamin
Math is logical, functional and just … awesome. Mathematician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series.
The Fibonacci Sequence – Golden Ratio and The Fractal Nature of Reality
Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.