Is the following the answer? If the triangle is equilateral, then all points inside the triangle serve (and all points outside if you assign signs to the distances). Otherwise the point is at the vertex with the largest angle. R. On Sat, 29 Oct 2011, Fred lunnon wrote:
Nice one, Dan --- bet that isn't in Clark Kimberling's list! WFL
On 10/28/11, Dan Asimov <dasimov@earthlink.net> wrote:
Given an arbitrary triangle T in R^2, characterize p in R^2 such that the sum of distances
S(p) := d(p, L_1) + d(p, L_2) + d(p, L_3)
is minimized, where the L_j are the affine lines containing the sides of T.
--Dan
"Things are seldom what they seem." --W.S. Gilbert
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