[OT] pythageoron and 3d

[Gwaihir]

just keep adding sides squared under the sqrt.

because the first diagonal is used as a side with the next "rectangular" side, so it looks like this (where a, b, c are the height, length, width, and you want the diagonal of the box):

diagonal of a side:
sqrt( a^2 + b^2 )

diagonal of box = diagonal of (diagonal of side & height):
sqrt( sqrt( a^2 + b^2 )^2 + c^2 )
=sqrt( a^2 + b^2 + c^2 )

so in an n-dimensional space, the distance from point p to point q is

sqrt( (p.1-q.1)^2 + (p.3-q.3)^2 + (p.3-q.3)^2 + . . . + (p.n-q.n)^2 )

(grr, how do you get &#nbsp; spaces to work? I can't do sigma notation without spaces to align the sub and superscritps. hrmph.)

hope that helps

edit: hehe, looks like i was beaten to it while i posted.

[ April 30, 2003, 00:38: Message edited by: Gwaihir ]