# Why two symbols for the Golden Ratio?

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

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

## 1 Answer

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

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