--- On Tue, 5/27/08, N. J. A. Sloane <njas@research.att.com> wrote:
From: N. J. A. Sloane <njas@research.att.com> Subject: Re: [math-fun] golden To: math-fun@mailman.xmission.com Date: Tuesday, May 27, 2008, 9:34 AM there are millions of places where "phi" is used and where "tau" is used for (1+sqrt(5))/2 ! it is too late to try to unify the notation, sorry!
Neil
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Fie on tau. Why do you think they're called phibonaccis? Macsyma even has FIBTOPHI, which transforms the fibs in an expression to powers of phi and 1-phi. Which I just used to prove that f[m-n]*f[m+n] = f[m+1]*f[m-1]*f[n]^2 - f[n+1]*f[n-1]*f[m]^2, where f[n]:=fib[n]*(-1)^binom(n,2). This plus gcd(f[n],f[m]) = |f[gcd(n,m)]| makes f a strong elliptic divisibility sequence (Not in MathWorld?). Likewise fib[n]*(-1)^binom(n-1,2), but no other asSIGNation (mod scaling). I fib you not. Dan> How about _x_ := floor(x) ? Neat, but then abs(floor(x)) will snare some unwaries. --rwg PS, in IE, when you roll over the equation displays in www.tweedledum.com/rwg/idents.htm, you see "micropopups" with bits of alternate text (Marginal Melvins). Is right click, Properties the only way to see even one of these with Firefox? (Sorry about the spamdangles--freeshell is down)