Polar duality and the generalized Law of Sines

Abstract.

A geometric formulation of the generalized Law of Sines for simplices in constant curvature spaces is presented. It is explained how the Law of Sines can be seen as an instance of the so-called polar duality, which can be formulated as a duality between Gram matrices representing the simplex.

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1. Department of Mathematics, Technical University of Denmark, 2800, Lyngby, Denmark

   Simon L. Kokkendorff

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1. Simon L. Kokkendorff
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Correspondence to Simon L. Kokkendorff.

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The work was supported by Enterprise Ireland.

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Kokkendorff, S.L. Polar duality and the generalized Law of Sines. J. geom. 86, 140–149 (2007). https://doi.org/10.1007/s00022-006-1858-7

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• Received: 02 March 2005

• Revised: 11 July 2006

• Issue Date: April 2007

• DOI: https://doi.org/10.1007/s00022-006-1858-7

Mathematics Subject Classification (2000):

• 51M20
• 52A55
• 52B11

Keywords:

• Constant curvature
• Gram matrix
• simplices
• Law of Sines
• polar duality
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