[note from moderator: several replies were received on this item - which is admittedly off-topic; they are digested below.] There are a number of books on the subject - or on the related Fibonacci numbers - which call it "the golden ratio", "the golden number", "the divine proportion", as well as phi. (Check out Amazon for example.) I think the name isn't as "fixed" as pi, e, or i, but it's pretty standard, within a small orbit. (Maple doesn't know it - unlike Pi!) Actually, in a sense, i isn't as standard as pi or e - at least in engineering circles, some prefer J (or j). (I've never seen a *mathematical* writer use J though - anyone?) Of course there are lots of non-real, non-complex, numbers with universally accepted one-letter symbols. (omega ... do you allow subscripts?) But real or complex? (And presumably not constants from physics ...) No others spring to mind, though I'm willing to bet that 5 minutes after I hit "send" one will do so! Close? There are a few, like the Euler constant gamma (lim_{n->\infty} (sum_{k=1}^n 1/k - ln n), but I suspect most mathematicians would have to look such cases up, so they hardly qualify. (I only know about gamma because it came up in conversation this past semester at work!) -= rags =- On Sat, 29 May 2004, Oswald Wyler wrote:
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
-- <rags@math.mcgill.ca> <www.math.mcgill.ca/rags> ------------------------------------------------------------------------------ From: Robert Knighten <Robert@Knighten.org> Date: Sun, 30 May 2004 16:46:52 -0700 I have no idea if you've missed something, but at least in the English speaking world \phi as the name for the golden ratio has indeed become the "accepted symbol". Asking Google about 'phi number "golden ratio"' produced 8120 pages containing all of those. This includes, for example, A biography of the number phi: The Golden Ratio: The Story of Phi: The World's Most Astonishing Number Mario Livio Broadway Books, 320 pp, $24.95 I don't know if the use of \phi for the golden ratio is common in other languages, but I suspect the pervasive effect of the English usage has had its effect. -- Bob -- Robert L. Knighten Robert@Knighten.org ----------------------------------------------------------------------- Date: Sun, 30 May 2004 19:05:29 -0400 From: Steve Stevenson <steve@cs.clemson.edu> This month's "Discover" magazine had an article on the golden ratio. steve ---------------------------------------------------------------------- Date: Mon, 31 May 2004 10:21:41 -0300 From: "Robert J. MacG. Dawson" <Robert.Dawson@smu.ca> As a generalization: "Golden ratio" is used by geometers being informal, autodidacts, historians, popular math writers, and crackpots. $\phi$ is used by popular math writers, autodidacts, and the better class of crackpots. $\tau$ is used by most mathematicians. A not-entirely-correct analogy: golden ratio:$\phi$:\tau$ :: blue vitriol : copper sulphate: copper(II) sulphate pentahydrate -Robert Dawson ------------------------------------------------------------------------------------ Date: Mon, 31 May 2004 10:29:36 -0400 (EDT) From: Peter Freyd <pjf@saul.cis.upenn.edu> Subject: "phi and gamma" Oswald Wyler writes: I have only met three real or complex numbers with universally accepted one-letter symbols: \pi, e, i. Have I missed something? Going by today's final arbiter of the universal, Google switches into calculator mode when queried for "e", "phi" and "pi" (delivering for each its numerical value to 8 decimal places -- it also names "phi" as "the golden ratio"). Google does not switch into calculator mode for "gamma" or "i" but it does for "1*gamma" (naming it as "1 * Euler's constant") and "1*i" (with no name). If you're willing to count dimensioned numbers then it also recognizes (and names) "c", "h", "k", and "u" if, in each case, you preface it with "1*". If you go beyond single letters then who knows? A few I've found are "1*au", "1*googol" and "1*mark twain". (Alas, Google has not yet learned to recognize "1*millihelen".) ------------------------------------------------------------------------ Date: Mon, 31 May 2004 10:12:38 -0700 (PDT) From: "John Baez" <baez@math.ucr.edu> I don't know what this has to do with categories, but it gives me the chance to recycle some trivia I recently learned. This number 1.618... is widely called phi, but also Phi - and also tau. It was named Phi after the Greek sculptor Phidias, who helped design the Parthenon. But it was named this only in 1914, in a book called The Curves of Life, by the artist Theodore Cook. And it was Cook who first started calling 1.618... the golden ratio! Before him, 0.618... was called the golden ratio. Cook dubbed this number "phi", the lower-case baby brother of Phi. In fact, the whole "golden" terminology can only be traced back to 1826, when it showed up in a footnote to a book by one Martin Ohm, brother of Georg Ohm, the guy with the law about resistors. Before then, a lot of people called 1/G the "Divine Proportion". And the guy who started that was Luca Pacioli, a pal of Leonardo da Vinci who translated Euclid's Elements. In 1509, Pacioli published a 3-volume text entitled Divina Proportione, advertising the virtues of this number.
So far, I have only met three real or complex numbers with universally accepted one-letter symbols: \pi, e, i. Have I missed something?
Sure - the Euler-Mascheroni constant, gamma = 0.5772156649015... = lim_{n->infinity} (integral_1^n dx/x) - (1/1 + 1/2 + ... + 1/n) See: http://mathworld.wolfram.com/Euler-MascheroniConstant.html By the way, engineers often call i "j". Best, jb