In article , "PDQ" wrote:
If you mean a miter cut, the length of the miter is

the root of two times the square of the width of the board.

Try again. Square root of 2 times the width of the board _not_ squared.

If you mean a bevel cut, the length of the bevel is

the root of two times the square of the thickness of the board.

Try again. Square root of 2 times the thickness of the board _not_ squared.
Your formulas below are correct (even though given with an absurd degree of
precision), but your descriptions above are wrong, and don't match the
formulas.

1 inch wide = 1.4142135623730950488016887242097
2 inch wide = 2.8284271247461900976033774484194
3 inch wide = 4.24264068711928514640506617262909
4 inch wide = 5.65685424949238019520675489683879

It appears the bevel/miter is proportional to the width by a factor of =
~1.41.

Yes. Proportional to the width. Not to the square of the width.

Or, the width/thickness is always 70.7106781186547524400844362105198% of
the bevel/miter.

70.7 % is plenty close enough.

--
Regards,
Doug Miller (alphageek at milmac dot com)

Nobody ever left footprints in the sands of time by sitting on his butt.
And who wants to leave buttprints in the sands of time?