On Tue, 8 Oct 2002, Ben wrote:
> On Tue, Oct 08, 2002 at 12:11:38PM +0100, Shevek wrote:
> > Metric space theory tells you that your distance computation is valid
> > whether you square or not. It's still a valid metric. The unit ball is a
> > slightly different shape ...
>
> Nonsense.
>
> d(x,y) = (x1 - y1)^2 + (x2 - y2)^2 + (x3 - y3)^2
>
> and
>
> g(x,y) = sqrt d(x,y)
>
> have precisely the same unit ball.
Actually I was referring (with much gesticulation) to different metrics
having different balls, but ... yes, in this case you are right.
The point being you don't need to square either, in which case you do get
a different ball.
S.
--
Shevek
I am the Borg.
sub AUTOLOAD{my$i=$AUTOLOAD;my$x=shift;$i=~s/^.*://;print"$x\n";eval
qq{*$AUTOLOAD=sub{my\$x=shift;return unless \$x%$i;&{$x}(\$x);};};}
foreach my $i (3..65535) { &{'2'}($i); }
