Golden ratio
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The golden ratio, golden number, golden section (when applied to the division of a line) or φ has been known for millennia. It is defined as "the ratio between two numbers such that the lesser is to the greater as the greater is to the sum"
A:B = B:(A+B)
B:A = φ = 1.61803398874989484820458683436563811772030917980576 (approx)
Its exact value is 
.
It has generally been thought to be pleasing and harmonious to human perception and is the basis of much classical architecture. The usage of the Greek letter phi to represent the golden ratio was suggested by mathematician Mark Barr from the first letter of Phidias (ancient Greek, Φειδίας), the sculptor who was alleged to have used it in creating statues for the Parthenon.
The golden number (or an approximation) appears often in nature and is the convergent point of the ratio of successive terms of the Fibonacci sequence - 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,....
| 1/1 | = | 1.000000 |
| 2/1 | = | 2.000000 |
| 3/2 | = | 1.500000 |
| 5/3 | = | 1.666666 |
| 8/5 | = | 1.600000 |
| 13/8 | = | 1.625000 |
| 21/13 | = | 1.615385 |
| 34/21 | = | 1.619048 |
| 55/34 | = | 1.617647 |
| 89/55 | = | 1.618182 |
| 144/89 | = | 1.617978 |
| 233/144 | = | 1.618056 |
| 377/233 | = | 1.618026 |
| 610/377 | = | 1.618037 |
| 987/610 | = | 1.618033 |
It is interesting to note that: Golden Ratio - 1 = 1/ Golden Ratio (by definition, of course).
[edit] Footnotes
- The Golden Ratio: The Story of Phi, The World's Most Astonishing Number by Mario Livio, 2002
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