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October 11, 2022 18:00–19:30
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On a method for calculating the volumes of polyhedra in hyperbolic space.
V. A. Krasnov Peoples' Friendship University of Russia, Moscow
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Abstract:
The lecture is devoted to the method of calculating the volumes of polyhedra in hyperbolic space (given by the Poincare model in the upper half-space), proposed in 2013 by I.H. Sabitov.
In the first part of the talk, we will derive a formula for the volume of an arbitrary hyperbolic tetrahedron (in standard position) through the coordinates of its vertices.
In the final part, the volumes of the so-called cyclic and permutation polyhedra in the hyperbolic case will be studied.
The report will be accompanied by formulations of unsolved problems in the volume theory of non-Euclidean polyhedra. No special knowledge is required to understand the talk.
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