Difference between revisions of "Golden ratio"

Latest revision as of 11:53, 3 June 2018

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

• Analogy
• Architecture
• Composition (visual arts)
• Design
• Design elements and principles
• Elements of art
• Pattern
• Phi
• Proportionality (mathematics)
• Ratio
• Scale (ratio)
• Scaling (geometry)
• Visual arts

External links

• Golden ratio @ Wikipedia
• Mathematical Impressions: The Golden Ratio by George Hart
• The designer's guide to the Golden Ratio