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$\begingroup$

Why is it that both
$\phi$
and
$\tau$
are used to designate the Golden Ratio
$\frac{1+\sqrt5}2?$

  • 2
    I have never heard of $\tau$ denoting the Golden Ratio. Can you provide an example? – 2017-01-03
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    I too have only seen $\phi$ used for this – 2017-01-03
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    It is just a symbol, who cares? I can use the symbol $U:=\frac{1+\sqrt 5}2$. – 2017-01-03
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    What is $\tau$ ? Is it the reciprocal of $\phi$ ? – 2017-01-03
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    In some contexts, I have seen $\tau = 2 \pi$ – 2017-01-03
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    I saw the $\tau\quad$ version in a discussion of the Binet closed-form formula for a Fibonacci number (based upon its index). – 2017-01-03
  • 0
    Use of tau: *Introduction to Geometry* by H.S.M. Coxeter. ?Perhaps also in Martin Gardner's "Mathematical Games" column in *Scientific American* when he devoted the whole column to that book when it was newly published. – 2017-01-03
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    I saw $\tau$ yesterday in Conway and Guy _The Book of Numbers_. They did not mention $\varphi$ or $\phi$. – 2017-01-04
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    I guess I shall have to get used to multiple nicknames: Some who know me address me as "Loser" and others as "Mr. Wonderful." – 2017-01-04

1 Answers 1

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The Golden Ratio or Golden Cut is the number $$\frac{1+\sqrt{5}}{2}$$ which is usually denoted by phi ($\phi$ or $\varphi$), but also sometimes by tau ($\tau$).

Why $\phi$ : Phidias (Greek: Φειδίας) was a Greek sculptor, painter, and architect. So $\phi$ is the first letter of his name.

The symbol $\phi$ ("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6).

Why $\tau$ : The golden ratio or golden cut is sometimes named after the greek verb τομή, meaning "to cut", so again the first letter is taken: $\tau$.

Source: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio; MathWorld

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    \ Thank you. Could Mr. Livio have been pulling our legs? Given the constant's intimate relation to the (*F*)ibonacci series, my choice has to be $\phi.$ – 2017-01-04