<< 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. (Maybe someone more historically and/or notationally savvy than I could chime in here.)
One (unrealistic) way to avoid ambiguity might be to redefine the golden ratio as the element [(1+sqrt5)/2] of R/Z. (Where [x] here means the equivalence class of x mod Z, i.e., the coset x + Z.) Idea: since square bracket [x] to mean the greatest integer <= x has largely been replaced by the computer science notation |_x_|, perhaps we can standardize the notation at least in math-fun by using _x_ to mean floor(x) from now on. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele