On the Volume Formulas of Cones and Orthogonal Multi-cones in S n(1) and H n(—1)
Wu-Yi Hsiang
Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (1) : 1 -30.
On the Volume Formulas of Cones and Orthogonal Multi-cones in S n(1) and H n(—1)
In the study of n-dimensional spherical or hyperbolic geometry, n≥ 3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in S n(1) and H n(—1).
Hyperbolic geometry / Volume / 51M10 / 51M20
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