Re: Point on sphere greatest distance from given points

*To*: mathgroup at smc.vnet.net*Subject*: [mg104078] Re: Point on sphere greatest distance from given points*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 18 Oct 2009 05:27:44 -0400 (EDT)*Reply-to*: hanlonr at cox.net

loc = CityData[#, "Coordinates"] & /@ {"Chicago", "New York", "London"} {{41.840675, -87.679365}, {40.704234, -73.917927}, {51.5, -0.1166667}} dist[{lat_?NumericQ, long_?NumericQ}, loc_List] := Total[GeoDistance[{lat, long}, #] & /@ loc] Maximize[{dist[{lat, long}, loc], -90 <= lat <= 90, -180 < long <= 180}, {lat, long}] {5.32962*10^7,{lat->-41.0337,long->105.825}} Bob Hanlon ---- Kelly Jones <kelly.terry.jones at gmail.com> wrote: ============= 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.