Volume formulas for a spherical tetrahedron

Author:
Jun Murakami

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3289-3295

MSC (2010):
Primary 51M25; Secondary 52A38, 26B15

Published electronically:
January 20, 2012

MathSciNet review:
2917101

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Abstract | References | Similar Articles | Additional Information

Abstract: The present paper gives two concrete formulas for the volume of an arbitrary spherical tetrahedron that is in a 3-dimensional spherical space of constant curvature . One formula is given in terms of dihedral angles, and another one is given in terms of edge lengths.

**1.**Yunhi Cho and Hyuk Kim,*On the volume formula for hyperbolic tetrahedra*, Discrete Comput. Geom.**22**(1999), no. 3, 347–366. MR**1706606**, 10.1007/PL00009465**2.**A. Kolpakov, A. Mednykh and M. Pashkevich, Volume formula for a -symmetric spherical tetrahedron through its edge lengths, to appear in*Ark. Mat.***3.**John Milnor,*Collected papers. Vol. 1*, Publish or Perish, Inc., Houston, TX, 1994. Geometry. MR**1277810****4.**Jun Murakami and Akira Ushijima,*A volume formula for hyperbolic tetrahedra in terms of edge lengths*, J. Geom.**83**(2005), no. 1-2, 153–163. MR**2193233**, 10.1007/s00022-005-0010-4**5.**Jun Murakami and Masakazu Yano,*On the volume of a hyperbolic and spherical tetrahedron*, Comm. Anal. Geom.**13**(2005), no. 2, 379–400. MR**2154824****6.**Akira Ushijima,*A volume formula for generalised hyperbolic tetrahedra*, Non-Euclidean geometries, Math. Appl. (N. Y.), vol. 581, Springer, New York, 2006, pp. 249–265. MR**2191251**, 10.1007/0-387-29555-0_13

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Additional Information

**Jun Murakami**

Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Email:
murakami@waseda.jp

DOI:
https://doi.org/10.1090/S0002-9939-2012-11182-7

Keywords:
Tetrahedron,
volume,
spherical space

Received by editor(s):
November 27, 2010

Received by editor(s) in revised form:
March 29, 2011

Published electronically:
January 20, 2012

Additional Notes:
This research was partially supported by Grant-in-Aid for Scientific Research(C) 22540236 from JSPS

Communicated by:
Jianguo Cao

Article copyright:
© Copyright 2012
American Mathematical Society