Point on sphere greatest distance from given points

*To*: mathgroup at smc.vnet.net*Subject*: [mg104054] Point on sphere greatest distance from given points*From*: Kelly Jones <kelly.terry.jones at gmail.com>*Date*: Sat, 17 Oct 2009 07:02:46 -0400 (EDT)

How can I use Mathematica to solve this problem: Given n points on a sphere, I want to find a point x such that: Sum[distance[x,i],{i,1,n}] is maximal, where "distance" is spherical ("great circle") distance. In other words, I want to find the point x "furthest" from the given n points. Is there any chance x will coincide with one of the given points? If so, is there a better notion of distance to use? -- We're just a Bunch Of Regular Guys, a collective group that's trying to understand and assimilate technology. We feel that resistance to new ideas and technology is unwise and ultimately futile.