The Golden Ratio (φ)
The ratio (about 1.618) you get when a line is divided so the whole is to the larger part as the larger part is to the smaller — often claimed to underlie classical beauty.
Origin
First written about by Euclid around 300 BCE as 'the extreme and mean ratio.' Renaissance mathematician Luca Pacioli published Divina Proportione in 1509, illustrated by Leonardo da Vinci, calling the ratio divine. It is related to the Fibonacci sequence: the ratio of consecutive Fibonacci numbers converges on φ. Claims that the Parthenon, the Mona Lisa, and Apple's logo were designed using the golden ratio are mostly retrofitted myth — the math is real, the design intent usually isn't.
Modern usage
Standard reference in design, photography, and architecture for 'pleasing proportion.' The Fibonacci-spiral overlay is the Instagram-design influencer's favorite tool. Often invoked as a mystical bridge between math and beauty; debunkers point out that many proportions in the human body and nature are not actually φ.
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