To accurately determine a diagonal distance when you know the
distance of two perpendicular edges, you can apply the
Pythagorean theorum. Given perpendicular edges with lengths a
and b, just square a, square b, and take the square root to get
the final length. (Image from the "Pythagorean theorem" article
at Wikipedia.) It turns out that calculating this is moderately
common for tabletop games played on a grid. However, people may
not have a calculator handy, so there are simpler solutions
designed to give a good enough approximation. I was curious how
accurate these approximations were. Percentage error for various
estimation systems: |1.5 long
diagonals||11.80%||8.93%||9.71%||10.00%| |New York
blocks||41.42%||29.85%||34.25%||34.16%| These were calculated by
considering every possibility for integer distances from 1
through 100 for each of the two orthogonal edges. Actual
Calculated using the Pythagorean theorum. 1.5 long diagonals Add
the length of the longer orthogonal edge to half of the length
of the oth