Abstract
Let S d-1 denote the (d − 1)-dimensional unit sphere centered at the origin of the d-dimensional Euclidean space. Let 0 < α < π. A set P of points in S d-1 is called almost α-equidistant if among any three points of P there is at least one pair lying at spherical distance α. In this note we prove upper bounds on the cardinality of P depending only on d.
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REFERENCE
M. Rosenfeld, Almost orthogonal lines in E d, in the The Victor Klee Festschrift, DIMACS Ser. in Disc. Math. and Th. Comp. Sci., Vol. 4, 1991.
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Bezdek, K., Lángi, Z. ALMOST EQUIDISTANT POINTS ON S D-1 . Periodica Mathematica Hungarica 39, 139–144 (2000). https://doi.org/10.1023/A:1004851109255
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DOI: https://doi.org/10.1023/A:1004851109255