Split any length by the golden ratio (φ ≈ 1.618) — useful in design, architecture, art and photography.
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The golden ratio (φ ≈ 1.618) splits a length into two parts: the whole is to the longer part as the longer part is to the shorter.
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The golden ratio splits a quantity so that the whole is to the larger part as the larger part is to the smaller. The golden number is:
For a length of 100: larger part = 100 ÷ φ ≈ 61.8, smaller part ≈ 38.2. The ratio 61.8 ÷ 38.2 ≈ 1.618.
A special ratio, about 1.618, where the whole relates to the larger part exactly as the larger part relates to the smaller. It is written with the Greek letter φ (phi).
φ = (1 + √5) ÷ 2 ≈ 1.6180339887. It is an irrational number with infinitely many decimals.
Larger part = length ÷ φ, and smaller part = length − larger part. For 100: larger ≈ 61.8, smaller ≈ 38.2.
The ratio of two consecutive Fibonacci numbers (1, 1, 2, 3, 5, 8, 13…) gets closer and closer to φ as the numbers grow.
Visual composition, architecture, logos and layout, as it is considered aesthetically pleasing. E.g. the Parthenon, Renaissance works, modern interfaces.
A rectangle whose side ratio is φ. If you remove a square from it, the remaining rectangle has the same proportions.
Split the frame by φ (instead of the rule of thirds) and place important elements on the resulting lines for a pleasing visual balance.
From the equation defining the golden ratio: φ² = φ + 1. Solving this quadratic gives the value (1 + √5) ÷ 2.