SharkD wrote:

> Actually, you were correct to begin with!!!! :) I looked at it again and
> realized the method I described only reproduces the "isometric" pattern of
> intersecting lines (which is sufficient for my needs). To reproduce the actual
> *hexagon* in its entirety you need to take things a step further:

So we're back with sqrt(3)/2 (or 2/sqrt(3)) ?

> Thanks for the tip! I was hoping for an algorithmic approach, but I guess
> there's no real need to go to all that effort.
> 

This is what I did:

% perl -e 'my $fmin = 10; for (my $n = 1; $n < 10000; $n ++) { my $m = int(sqrt(3) / 2
* $n + 0.5); my $f = abs( $m / $n / (sqrt(3) / 2) - 1); if ($f < $fmin) { $fmin = $f;
$n0 = $n; $m0 = $m; printf "%6d %6d %g\n", $n0, $m0, $fmin } }'

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