Difference between revisions of "Golden ratio"
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| − | In [[mathematics]], two quantities are in the [[golden ratio]] if their ratio is the same as the [[ratio]] of their [[Summation|sum]] to the larger of the two quantities. | + | In [[mathematics]], two quantities are in the [[golden ratio]] if their [[ratio]] is the same as the [[ratio]] of their [[Summation|sum]] to the larger of the two quantities. |
== Names == | == Names == | ||
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* Golden cut | * Golden cut | ||
* Golden number | * Golden number | ||
| + | |||
| + | == Nature == | ||
| + | |||
| + | The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other [[plant]] parts. | ||
| + | |||
| + | == History == | ||
| + | |||
| + | 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. | ||
| + | |||
| + | == Architecture == | ||
| + | |||
| + | Some twentieth-century [[Artist|artists]] and [[Architect|architects]], including [[Le Corbusier]] and [[Dalí]], 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. | ||
| + | |||
| + | == Applications == | ||
| + | |||
| + | The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets. | ||
== See also == | == See also == | ||
* [[Analogy]] | * [[Analogy]] | ||
| + | * [[Pattern]] | ||
* [[Proportionality (mathematics)]] | * [[Proportionality (mathematics)]] | ||
| + | * [[Ratio]] | ||
| + | * [[Ratio (mathematics)]] | ||
* [[Scaling (geometry)]] | * [[Scaling (geometry)]] | ||
Revision as of 18:41, 20 February 2016
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
Names
The golden ratio also is called:
- Golden mean
- Golden section (Latin: sectio aurea).
- Extreme and mean ratio
- Medial section
- Divine proportion
- Divine section (Latin: sectio divina)
- Golden proportion
- Golden cut
- Golden number
Nature
The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.
History
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.
Architecture
Some twentieth-century artists and architects, including Le Corbusier and Dalí, 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.
Applications
The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets.
See also
External links
- Golden ratio @ Wikipedia
