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Stability Configurations of Electrons on a Sphere


Author: Michael Goldberg
Journal: Math. Comp. 23 (1969), 785-786
DOI: https://doi.org/10.1090/S0025-5718-69-99642-2
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Abstract | References | Additional Information

Abstract: Stable arrangements of electrons in equilibrium on the surface of a sphere have been obtained for most of the cases up to 14 electrons. They resemble the arrangements of the contact points of the faces of an $ n$-hedron of least volume circumscribed about the sphere, except for $ n = 8$. In this case, it is shown that the electrons near the contact points are in equilibrium, but the arrangement is not stable.


References [Enhancements On Off] (What's this?)

  • [1] L. Föppl, ``Stabile Anordnungen von Elektronen im Atom,'' J. Reine Angew. Math., v. 141, 1912, pp. 251-301.
  • [2] H. Cohn, ``Stability configurations of electrons on a sphere,'' MTAC., v. 10, 1956, pp. 117-120. MR 18, 356. MR 0081133 (18:356l)
  • [3] M. Goldberg, ``The isoperimetric problem for polyhedra,'' Tôhoku Math. J., v. 40, 1935, pp. 226-236.


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-69-99642-2
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society