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Number & MeasureGreekEnglish

Phi

/faɪ/noun

The twenty-first letter of the Greek alphabet, used as a symbol for the golden ratio, for angles, and for magnetic flux.

The Greek roots

φεῖ
pheî
the letter phi

Literally: the Greek letter ph

Follow a root:φεῖ1 word

The story of the word

In classical Attic the letter was an aspirated p, not the f sound English gives it, which is why Roman scribes wrote it as ph rather than f. Its fame as the golden ratio is barely a century old: Mark Barr proposed φ in the early 1900s, choosing the initial of Phidias, who built the Parthenon sculptures. Euclid had described the same proportion without any symbol at all, calling it division in extreme and mean ratio.

How it travelled
Ancient Greek → Latin → English

In a sentence

He wrote phi on the board and drew the rectangle before anyone could ask what it meant.

The totient function is written with a phi, which trips up students who expect the golden ratio.

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