On a method of volume calculation for bodies
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 615-626.

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In this paper we propose some integral formulae for volumes of bodies with known boundaries in the spaces of constant curvature of arbitrary dimension with some examples of their applications.
Keywords: models of spaces of constant curvature, prizmo- and ball-like bodies
Mots-clés : volumes and algebraic volumes, polygons, symplices.
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I. Kh. Sabitov. On a method of volume calculation for bodies. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 615-626. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a33/

[1] I. Kh. Sabitov, Chemu ravna summa uglov mnogougolnika?, Kvant, 3 (2001), 6–12

[2] B. A. Rozenfeld, Neevklidovy prostranstva, Nauka, M., 1969 | MR

[3] D. V. Alekseevskii, E. B. Vinberg, A. S. Solodovnikov, “Geometriya prostranstv postoyannoi krivizny”, Geometriya – 2, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 29, VINITI, M., 1988, 5–146

[4] D. A. Derevnin, A. D. Mednykh, “O formule ob'ema giperbolicheskogo tetraedra”, UMN, 60:2 (2005), 159–160 | DOI | MR

[5] Á. G. Horváth, “Formulas on hyperbolic volume”, Aequationes mathematicae, 83:1–2 (2012), 97–116 | DOI | MR | Zbl