Arrangements of 13 points on a sphere
Károly J. Böröczky, László E. Szabó · SZTAKI Publication Repository (Hungarian Academy of Sciences) · 2003
KAROLY BOROCZKY 1 Department of Geometry, Eotvos Lorand University, H-1117 Budapest, Pazmany Peter setany 1/cLASZLO SZABO 2 Computer and Automation Research Institute, Hungarian Academy of Sciences, H-1111 Budapest, Lagymanyosi utca 11ABSTRACT. Let a k denote the maximum number with the property that onecan place k points on the unit sphere so that the spherical distance between any two different points is at least a k . 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 are concerned with the first unsolved case k=13 which is particularly interesting because of its close relation to several famous problems in discrete geometry. Acertain arrangement of 13 points on shows that a 13=0.997223592…. On the other hand K.Schutte and B.L. van der Waerden proved that…. In this paper we prove that a 13<1.02746114.