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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?

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