Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Stability Configurations of Electrons on a Sphere

Author: Michael Goldberg
Journal: Math. Comp. 23 (1969), 785-786
Full-text PDF Free Access

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

Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society