Difference between revisions of "Golden ratio"
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Its exact value is <math>\varphi=\frac{1+\sqrt5}{2}</math>.<br /> | Its exact value is <math>\varphi=\frac{1+\sqrt5}{2}</math>.<br /> | ||
| − | It has generally been thought to be pleasing and ''harmonious'' to human perception | + | It has generally been thought to be pleasing and ''harmonious'' to human perception. 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,.... | 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,.... | ||
Revision as of 03:59, 18 March 2010
Template:Sci-outline The golden ratio (also referred to as the golden number or golden section) 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. 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: (by definition, of course).
Some people think that the golden ratio is an ideal way to proportion loudspeaker cabinets, but what do they know?
Footnotes
- The Golden Ratio: The Story of Phi, The World's Most Astonishing Number by Mario Livio, 2002
