Arrangements of 14, 15, 16 and 17 points on a sphere-Reference-Cited by-同舟云学术

Arrangements of 14, 15, 16 and 17 points on a sphere

Published:2003-10-01 Issue:4 Volume:40 Page:407-421
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:

Author:

Böröczky Károly¹,Szabó László²

Affiliation:

1. 1 Eötvös Loránd Tudom\ányegyetem, Természettudományi Kar, Geometria Tanszék Pázmány Péter Sétány 1/C, H-1117 Budapest, Hungary

2. 2 Magyar Tudományos Akadémia, Számítástechnikai és Automatizálási Kutatóintézet Postafiók 63, H-1518 Budapest, Hungary

Abstract

Let ak denote the maximum number with the property that one can place k points on the unit sphere S2 so that the spherical distance between any two different points is at least ak. The exact value of ak is determined only for some small values of k, namely, for k = 12 and k=24. In this paper we give new upper bounds on ak for k=14,15,16,17.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/sscmath.40.2003.4.3

Reference11 articles.

1. Arrangement of 24 points on a sphere;R. Robinson;Math. Ann.,1961

2. Endliche Punktmengen auf der 2-Sphäre mit möglichst großem Minimalabstand. Habilitationsschrift, Universität Göttingen, 1963. (English translation: Finite point-sets on S² with minimum distance as large as possible;L. Danzer;Discrete Math.,1963

3. Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems;L. Fejes;Jber. Deutsch. Math. Verein.,1943

4. On the densest packing of spherical caps;L. Fejes;Amer. Math. Monthly

5. The Tammes problem for n = 10;L. Hárs;Studia Sci. Math. Hungar.,1986

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Towards a proof of the 24-cell conjecture;Acta Mathematica Hungarica;2018-04-24

2. Configuration Spaces of Equal Spheres Touching a Given Sphere: The Twelve Spheres Problem;Bolyai Society Mathematical Studies;2018

3. Five Essays on the Geometry of László Fejes Tóth;Bolyai Society Mathematical Studies;2018

4. Covering the sphere by equal zones;Acta Mathematica Hungarica;2016-05-19

5. The Tammes Problem for N = 14;Experimental Mathematics;2015-07-20