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. Expressed algebraically, for quantities ⁠ ⁠ and ⁠ ⁠ with ⁠ ⁠, ⁠ ⁠ is in a golden ratio to ⁠ ⁠ if. where the Greek letter phi (⁠ ⁠ or ⁠ ⁠) denotes the golden ratio.

Phi ( Φ = 1.618033988749895… ), most often pronounced fi like “fly,” is simply an irrational number like pi ( p = 3.14159265358979… ), but one with many unusual mathematical properties. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation.

The golden ratio (symbol is the Greek letter phi shown at left) is a special number approximately equal to 1.618 ... It appears many times in geometry, art, architecture and other

2012年5月16日 · Phi, Φ, 1.618…, has two properties that make it unique among all numbers. If you square Phi, you get a number exactly 1 greater than itself: 2.618…, or Φ² = Φ + 1. If you divide Phi into 1 to get its reciprocal, you get a number exactly 1 less than itself: 0.618…, or 1 …

2024年4月13日 · Golden Ratio, Golden Mean, Golden Section, or Divine Proportion refers to the ratio between two quantities such that the ratio of their sum to the larger of the two quantities …

2019年11月25日 · The number phi, often known as the golden ratio, is a mathematical concept that people have known about since the time of the ancient Greeks. It is an irrational number like pi and e, meaning...

The golden ratio, 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 .

2012年5月13日 · It wasn’t until the 1900’s that American mathematician Mark Barr used the Greek letter phi (Φ) to designate this proportion. This appeared in the “The Curves of Life” (page 420) in 1914 by Theodore Andrea Cook . By this time this ubiquitous proportion was known as the golden mean, golden section and golden ratio as well as the Divine proportion.

Phi (Φ, φ) is the 21st letter of the Greek alphabet. In the system of traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ). In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voiceless bilabial plosive ( [p h]), which was the origin of its usual romanization as ph .

In Mathematics, golden ratio – also known as golden mean, golden section, divine proportion – is a special number, which is often represented using the symbol “ϕ” (phi). The golden ratio finds its application in various fields such as arts, architecture, geometry, and so on.