Polar duality and the generalized law of sines. (English) Zbl 1115.51010
Summary: 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.
MSC:
51M20 | Polyhedra and polytopes; regular figures, division of spaces |
52A55 | Spherical and hyperbolic convexity |
52B11 | \(n\)-dimensional polytopes |