On Wed, 10 Jul 2002, Nicholas Clark wrote:
> > Dan Sugalski wrote:
>
> > > Heh. I never expected to have to dust off my trig skills when I
> > > started this. If I need to dig out the calculus books, I think I'll
> > > just go run screaming...
>
> Unless I'm being thick, x² < y² whenever x < y for positive x and y
> (ie you don't need to take the square root of the hypotenuse to work out which
> hypotenuse is shorter. And all we're actually interested in which one is
> shorter, aren't we?)
(Assuming, of course, that |x| and |y| are both >= 1, which is obviously
true here since they are integers. (That's the sort of trick they like to
put in the SAT math section.))
Assuming x and y are coordinates in a 2-d space, and that both are
integers >= 0, why not just use what is affectionately called the
"taxicab" metric: x+y? It is just as "valid" and even quicker to
compute than the Euclidean metric sqrt(x^2 + y^2).
Of course the ordering of which is "closer" is different depending on the
metric chosen -- which is partly my point. If the actual result obtained
from a calculation would differ in any significant way depending on which
metric were used, then it might be a warning sign that there's a
higher-level problem at hand.
Practically, of course, any metric is fine for the moment -- it can always
be changed later if warranted.
--
Andy Dougherty [EMAIL PROTECTED]
Dept. of Physics
Lafayette College, Easton PA 18042
