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.

2015年7月12日 · This “golden” number, 1.61803399, represented by the Greek letter Phi, is known as the Golden Ratio, Golden Number, Golden Proportion, Golden Mean, Golden Section, Divine Proportion and Divine Section.

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 / Φ = Φ - 1.

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 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.

最著名的例子是優選學的黃金比法或0.618法，是由美國數學家 杰克·基弗 （英语：Jack Kiefer (statistician)） 於1953年首先提出，70年代在中國推廣。 黃金分割 是根據 黃金比例，將一條線分割成兩段。 總長度 a+b 与長度較長的 a 之比等于 a 与長度較短的 b 之比. 兩個數值 和 構成黃金比例 ，如果： 一個得出 數值的方法是從左邊的分數式入手。 經過簡化和代入， 於是： 兩邊乘以 就得到： 即是. 找出 該 方程 的正解， 黄金比奇妙之處在於其 倒數 為自身減1， …

The golden ratio is a special ratio with approximate value 1.61803..., an irrational number. The golden ratio is typically denoted with the Greek letter, phi (φ), and has been studied by mathematicians throughout history, including Euclid (~300 BC).

4 天之前 · 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 …

2023年8月30日 · The golden section (Phi), simple defintions; its exact value and the first 2000 decimal places; finding the golden section using geometry (compass and ruler); a new form of fractions (continued fractions) and the golden section lead back to the Fibonacci numbers! Two simple tricks to find the golden section on your calculator.

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.