       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)

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.

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