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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
DOI: https://doi.org/10.1090/S0002-9939-2012-11182-7
Published electronically: January 20, 2012
MathSciNet review: 2917101
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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 $ +1$. One formula is given in terms of dihedral angles, and another one is given in terms of edge lengths.


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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