On Thu, Jul 11, 2002 at 01:18:51PM -0700, John Porter wrote: > Nicholas Clark wrote: > > I was thinking that the metric (x*x + y*y) would be fast to > > calculate, as that's all we need for ordering. > > Point is, it's rather *more* than we need for ordering. > x + y will suffice.
IIRC, all metrics of the form (x^n + y^n)^(1/n), n=1,2,...Inf are strongly equivalent, ie they give rise to the *same* ordering. (In the limit as n -> Inf, the metric is max(x,y).) -- A walk of a thousand miles begins with a single step... then continues for another 1,999,999 or so.
