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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
Posted:
January 20, 2012
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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.
References
- 1.
Yunhi
Cho and Hyuk
Kim, On the volume formula for hyperbolic tetrahedra, Discrete
Comput. Geom. 22 (1999), no. 3, 347–366. MR 1706606
(2000k:52008), http://dx.doi.org/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
(95c:01043)
- 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
(2006k:52012), http://dx.doi.org/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
(2006d:52007)
- 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
(2007h:52008), http://dx.doi.org/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:
http://dx.doi.org/10.1090/S0002-9939-2012-11182-7
PII:
S 0002-9939(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
Posted:
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
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