| If you have N points on the unit circle, then to get a stationary
point of the sum of the pairwise distances between the points,
a set of relations will have to be satisfied of the form
for 3 points at angles t1, t2, t3:
sin(t1 - t2) + sin(t1 - t3) = 0
sin(t2 - t1) + sin(t2 - t3) = 0
sin(t3 - t1) + sin(t3 - t2) = 0
for 4 points at angles t1-t4
sin(t1 - t2) + sin(t1 - t3) + sin(t1 - t4) = 0;
sin(t2 - t1) + sin(t2 - t3) + sin(t2 - t4) = 0;
sin(t3 - t1) + sin(t3 - t2) + sin(t3 - t4) = 0;
sin(t4 - t1) + sin(t4 - t2) + sin(t4 - t3) = 0;
and so on, it looks like by symmetry that they should be at the
vertices of a regular n-gon for at least one solution for case 4 and
beyond.
- Jim
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