Goleden Ratio

1. Definition

1.1. It is also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. It is denoted , or sometimes .

1.2. "phi" = Φ = (√5 + 1) / 2 = 1.618033988749894848204586834365638117720...

1.3. "phi" = 2cos(pi/5) = 1/2 sec(2pi/5) = 1/2 csc (pi/10)

2. Application

2.1. recurrence relation

2.2. connects continued fractions and the Euclidean algorithm

2.3. Aesthetics

2.4. Architecture

2.5. Perceptual studies

2.6. Painting

2.7. Book design

2.8. Music

2.9. Industrial design

2.10. Nature

2.11. Optimization

2.12. Finance

3. The symbol ("phi") was apparently first used by Mark Barr at the beginning of the 20th century

4. History

4.1. The term "golden section" seems to first have been used by Martin Ohm in the 1835

4.2. The first known use of this term in English is in James Sulley's 1875 article