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Miklós Schweitzer
1956 Miklós Schweitzer
5
5
Part of
1956 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1956- Problem 5
Source:
10/9/2015
5. On a circle consider
n
n
n
points among which there acts a repulsive force inversely proportional to the square of their distance. Prove that the point system is in stable equilibrium if and only if the points form a regular
n
n
n
-gon; in other words, considering the sum of the reciprocal distances of the
(
n
2
)
\binom{n}{2}
(
2
n
)
pairs of points which can be chosen from among the
n
n
n
given points, this sum is minimal if and only if the points lie at the vertices of a regular
n
n
n
-gon. (G. 2)
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