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.
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.
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.
Or, the width/thickness is always 70.7106781186547524400844362105198% of the bevel/miter.
_________________________________________________________
Dougie, you said
 You missed the point rather dramatically, I'm afraid. You wrote that the width
 of the miter was proportional to "the square of the width of the board".
I don't think so. No where in the preceding, which I include herewith for clarity, did I state what you saw.
Better get your eyes checked. Your geekiness leaves much to be desired. You might, however, be in line for the "Conehead" awards.
________________________________________________________

PDQ

 >Picky, picky, picky.
 >
 >If you want to play those games, Doug:
 >
 >"Bevel" is described as "the angle formed at the juncture of two non =
 >perpendicular surfaces."
 >
 >"Miter" could mean "a tall ornamental liturgical headdress" worn by some =
 >members of the clergy, or it could mean, as it does in this case, =
 >"either of the surfaces that come together in a miter joint".
 >
 >If you want to play with polygonal surfaces, why not say so? "board =
 >_not_ squared" is so imprecise.
 >
 >I guess your problem must lie with your inability to visualize the =
 >position of the board within its frame of reference.

 You missed the point rather dramatically, I'm afraid. You wrote that the width
 of the miter was proportional to "the square of the width of the board".

 This is false.

 It is proportional to the *width* of the board. Period. Not the square of its
 width.

 You then compounded this error by repeating it with respect to thickness, and
 bevels.

 And now you've compounded it still further by showing that, in addition to
 your difficulties with mathematics, you also have some reading comprehension
 issues.

 
 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?