Thomson Problem Solutions

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In the Thomson problem, point charges are placed on the surface of a unit sphere in such a way as to minimize the total energy of the system. These solutions place each point so that its nearest neighbors are as far away as possible.


This Demonstration uses precalculated data from [1], which represents many years of research and optimization. Officially, the problem is only solved for 1 to 6 and 12 points; all other solutions are considered "best known." For code that solves the Thomson problem, see the Related Links.


Contributed by: Ed Pegg Jr (January 2016)
Open content licensed under CC BY-NC-SA




[1] D. J. Wales and S. Ulker. "Global Minima for the Thomson Problem." (Jan 4, 2016)

[2] Wikipedia. "Thomson Problem," (Jan 4, 2016)

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