From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2715 Path: news.gmane.org!not-for-mail From: Nils Andersen Newsgroups: gmane.science.mathematics.categories Subject: Re: \phi for the golden ratio? Date: Tue, 1 Jun 2004 09:21:10 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Trace: ger.gmane.org 1241018847 5451 80.91.229.2 (29 Apr 2009 15:27:27 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:27:27 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Jun 2 18:19:14 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 Jun 2004 18:19:14 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BVd5Z-0003N7-00 for categories-list@mta.ca; Wed, 02 Jun 2004 18:15:57 -0300 X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on nhugin.diku.dk Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 37 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:2715 Archived-At: [and one more...] In reply to the question from Oswald Wyler 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