       Crossing plane and cuboid

• To: mathgroup at smc.vnet.net
• Subject: [mg30236] Crossing plane and cuboid
• From: seidovzf at yahoo.com (Zakir F. Seidov)
• Date: Fri, 3 Aug 2001 00:56:05 -0400 (EDT)
• Organization: The Math Forum
• Sender: owner-wri-mathgroup at wolfram.com

Some times ago I thought on a lot
but could not find solution for the problem:
we have a cuboid (= parallelepiped) with edges a, b, c;
such that 0<x<a, 0<y<b, 0<z<c;
also we have a plane:
X/A + Y/B + Z/C = 1.

Values a, b, c, A, B, C are such that
plane crosses cuboid for sure,
.....................========

and I don't need generalized program
checking all weird cases...

What I need is a Mathematica program to calculate:
a) volumes of two parts of cuboid
b) area of cross-section

May be our dear Mathematica gurus
(I mean dear Mathematica and dear gurus)
can provide me with it.

Thank you very much.
Zakir

PS For more patient/interested people:
This is for the classical and unsolved yet
(according to Michael Trott)
problem of random tetrahedron in cube.
For more easy problem
of random triangle in square see

 M. Trott, Mathematica J., v7, i2, 189-197, 1998
 me, http:arxiv.org/abs/math.GM/0002134

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