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 [1] M. Trott, Mathematica J., v7, i2, 189-197, 1998 [2] me, http:arxiv.org/abs/math.GM/0002134