In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the "golden ratio". Stated as a decimal fraction, the golden ratio equals approximately 0.6180340. Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio.
Approximate logarithmic spirals can occur in nature (for example, the arms of spiral galaxies or phyllotaxis of leaves); golden spirals are one special case of these logarithmic spirals. Some twentieth-century artists and architects have proportioned their works to approximate the golden ratio — especially in the form of the golden rectangle — believing this proportion to be aesthetically pleasing.
The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data. The fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
Some twentieth-century artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Many designers are fond of its appearance, and the golden ratio or rectangle may be found in designs everywhere, including commercial graphics.
Text: Wikipedia and LWH
Shell Chris Akkana Peck via Wikimedia Commons
Leaf By Grupo Firenze via Wikimedia Commons
FInger Image courtesy of http://www.goldennumber.net, Gary B. Meisner, Copyright 2001-2013.