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}
}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.
204 Citations
Maximal packing density of n-dimensional Euclidean space with equal balls
- Mathematics
- 1975
An estimate δn ⩽ 2-n(0.5237+o(1)) is obtained for the maximal packing density of n-dimensional Euclidean space with equal balls for n→ ∞. This result is based on an improvement in a corresponding…
New Bounds on the Number of Unit Spheres That Can Touch a Unit Sphere in n Dimensions
- Computer ScienceJ. Comb. Theory, Ser. A
- 1979
NEW BOUNDS FOR DENSEST PACKING OF SPHERES IN n-DIMENSIONAL EUCLIDEAN SPACE
- Mathematics
- 1974
In this article we obtain an upper bound for the number of spherical segments of angular radius α that lie without overlapping on the surface of an n-dimensional sphere, and an upper bound for the…
The closest pair of N random points on the surface of a sphere
- Mathematics
- 1979
SUMMARY Consider N points distributed independently and uniformly on the surface of a sphere. Exact upper and lower bounds are found for the distribution of the smallest angular distance between…
Multiple Packing of the Euclidean Sphere
- MathematicsIEEE Trans. Inf. Theory
- 1999
We obtain the asymptotical bounds on the radius of the Euclidean sphere, such that any sphere with this radius contains not more, than L points from the subset of the unit Euclidean sphere.
On Packings of Spheres in Hilbert Space
- MathematicsProceedings 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…
Edge Close Ball Packings
- MathematicsDiscret. Comput. Geom.
- 2001
It is shown that the unique packing with minimal edge closeness is generated by the space centred cubic lattice.
New Bounds for Spherical Two-Distance Sets
- Mathematics, Computer ScienceExp. Math.
- 2013
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.
References
SHOWING 1-5 OF 5 REFERENCES
Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?
- Mathematics
- 1951
DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,…
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