The Closest Packing of Spherical Caps in n Dimensions

@article{Rankin1955TheCP,
  title={The Closest Packing of Spherical Caps in n Dimensions},
  author={Robert A. Rankin},
  journal={Proceedings of the Glasgow Mathematical Association},
  year={1955},
  volume={2},
  pages={139 - 144}
}
  • R. Rankin
  • Published 1 July 1955
  • Mathematics
  • Proceedings of the Glasgow Mathematical Association
Let Sn denote the “surface” of an n-dimensional unit sphere in Euclidean space of n dimensions. We may suppose that the sphere is centred at the origin of coordinates O, so that the points P(x1, x2, …, xn) of Sn satisfy We suppose that n≥2. 
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  • R. Rankin
  • Mathematics
    Proceedings of the Glasgow Mathematical Association
  • 1955
A point x in real Hilbert space is represented by an infinite sequence (x1, x2, x3, …) of real numbers such that is convergent. The unit “sphere“ S consists of all points × for which ‖x‖ ≤ 1. The
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TLDR
The semidefinite programming method is used to compute improved estimates of the maximum size of spherical two-distance sets, finding exact answers for dimensions n=23 and 40⩽n⦽93, where previous results gave divergent bounds.
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Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?
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Waerden, " Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand 1 Platz?
  • Math. Ann
  • 1951
mit Mindestabstand 1 Platz?
  • Auf welcher Kugel haben
  • 1951