Subject: categories: Re: \phi for the golden ratio?

From: Nils Andersen <[email-masked]>
Date: Tue, 1 Jun 2004 09:21:10 +0200

[and one more...]

In reply to the question from Oswald Wyler <[email-masked]>
let me quote from Donald E. Knuth, The Art of Computer Programming
(1968, 1973), Section 1.2.8:

The number $\phi$ itself has a very interesting history.  Euclid
called it the "extreme and mean ratio"; the ratio of A to B
is the ratio of (A+B) to A, if the ratio of A to B is $\phi$.
Renaissance writers called it the "divine proportion"; and in the
last century it has commonly been called the "golden ratio".  In
the art world, the ratio of $\phi$ to 1 is said to be the most
pleasing proportion aesthetically, and this opinion is confirmed
from the standpoint of computer programming aesthetics as well.
For the story of $\phi$, see the excellent article "The Golden
Section, Phyllotaxis, and Whythoff's Game", by H.S.M. Coxeter,
Scripta Math. 19 (1953), 135-143, and see also Chapter 8 of
The 2nd Scientific American Book of Mathematical Puzzles and Diversions,
by Martin Gardner (New York:  Simon and Schuster, 1961).

-- Nils Andersen

>In seventh or eighth grade -- a long time ago -- , I learned the name
>"goldener Schnitt" (golden ratio, ratio aurea) for the positive solution
>of the equation x^2 = x + 1.  Recently, I read an article, I forgot
>where, discussing this number and using \phi as the "accepted symbol"
>for it.  The old name was never mentioned.
>
>So far, I have only met three real or complex numbers with universally
>accepted one-letter symbols:  \pi, e, i.  Have I missed something?
>
>Oswald Wyler