Why is it that both
are used to designate the Golden Ratio

  • 2
    $\begingroup$ I have never heard of $\tau$ denoting the Golden Ratio. Can you provide an example? $\endgroup$ – pseudoeuclidean Jan 3 '17 at 14:23
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    $\begingroup$ I too have only seen $\phi$ used for this $\endgroup$ – MPW Jan 3 '17 at 14:24
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    $\begingroup$ It is just a symbol, who cares? I can use the symbol $U:=\frac{1+\sqrt 5}2$. $\endgroup$ – Masacroso Jan 3 '17 at 14:27
  • $\begingroup$ What is $\tau$ ? Is it the reciprocal of $\phi$ ? $\endgroup$ – Peter Jan 3 '17 at 14:31
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    $\begingroup$ In some contexts, I have seen $\tau = 2 \pi$ $\endgroup$ – pseudoeuclidean Jan 3 '17 at 14:40

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

  • $\begingroup$ \ 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 $\phi.$ $\endgroup$ – Senex Ægypti Parvi Jan 4 '17 at 17:32

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