Re: Balance point of a solid

*To*: mathgroup at smc.vnet.net*Subject*: [mg113781] Re: Balance point of a solid*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 12 Nov 2010 05:27:50 -0500 (EST)*References*: <iam332$jvn$1@smc.vnet.net> <ibgj10$ec3$1@smc.vnet.net>

On Nov 11, 3:11 am, Andreas <aa... at ix.netcom.com> wrote: > Daniel, Ray, Clifford -- Many thanks for the thought provoking > contributions. > > Ray and others have found using integration on this problem takes > inordinately long to calculate once you get to 5 dimensions. > > Could one attack this problem in another way? It occurred to me > that given that we know the lengths of the base simplex and heights > of the trapezoids as well as the right angles of the heights to the > base simplex one could then calculate the length of the top lines and > solve the entire thing geometrically without needing to integrate. > Not necessarily pretty or elegant but it might give give a solution > that calculates fast. > > Anyone think this could work? The solution I found, rewritten here in the notation of my Nov 5 post as ((h/Tr@h + 1)/(1 + Length@h)).A , is fast and agrees with the results given by integrating. What's missing is a proof.