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φ = 1.618... — the golden ratio
The golden ratio φ ≈ 1.618 appears in nature, art and architecture: spiral shells, sunflower heads, the proportions of the Parthenon and Da Vinci's Vitruvian Man. Fibonacci numbers approach φ when dividing consecutive terms.
Science
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Golden ratio in art and design
Logos of Apple, Twitter, National Geographic and many other brands are built on the golden ratio. Paintings by Botticelli, Leonardo and Salvador Dalí contain φ proportions. The brain perceives these proportions as 'perfectly beautiful'.
Culture
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'Divina Proportione' by Luca Pacioli — 1509
Luca Pacioli's treatise 'Divina Proportione' (1509), illustrated by Leonardo da Vinci, popularized the golden ratio during the Renaissance. Pacioli called φ the 'divine proportion' for its universality.
History