From: James Propp <jpropp@cs.uml.edu>
I believe that historically both (1+sqrt(5))/2 and its reciprocal (-1+sqrt(5))/2 have been called the golden ratio (maybe one is the golden ratio and the other is the golden section?), so it'd be handy if one of the two numbers were denoted phi and the other were denoted by tau.
From: "Fred lunnon" <fred.lunnon@gmail.com>
You're right about the ambiguity. I'd prefer to ignore (sqrt5 - 1)/2 though, on the grounds that the conjugate of tau = (1 + sqrt5)/2 is actually taubar = (1 - sqrt5)/2 = -1/tau, the negative of the smaller ratio. WFL
Wikipedia & Mathworld both say (1 - sqrt5)/2 is called the "golden ratio conjugate" & Mathworld adds "silver ratio". Wikipedia rationalizes (heh) that it's the absolute value of the actual conjugate. Both use the convention phi = (1+sqrt5)/2 and Phi = (1-sqrt5)/2, -+- / (|) or (/) capital Phi -+- / but Mathworld sez that Phi for the larger and phi the smaller "are sometimes also used (Knott), although this usage is not necessarily recommended." http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/ I have personally been fiddling with the number phi^-2 =~ .381966. Might as well call them phi, 1, pho, phoo. Which naturally extends to ...phooo, phoo, pho, 1, phi, phii, phiii... Although I don't know all the Greek letters for those. I do think we should redefine 1 as phi^0 and use the less confusing notation "ph". --Steve