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The Quarterly Journal of Mathematics Advance Access originally published online on June 29, 2006
The Quarterly Journal of Mathematics 2007 58(1):107-126; doi:10.1093/qmath/hal008
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

SPHERICAL SIMPLICES AND THEIR POLARS

Kenzi Satô

Department of Mathematics, Faculty of Engineering, Tamagawa University, 6-1-1, Tamagawa-Gakuen, Machida, Tokyo 194-8610, Japan

E-mail: kenzi{at}eng.tamagawa.ac.jp

Received 30 August 2005; revised 13 February 2006
  Abstract

This article is about spherical simplices in the unit sphere. One of the purposes is to give a relation of dihedral angles of a spherical simplex and its polar, and the other is to give two simple formulae of volumes of spherical simplices and their polars. We can calculate the volume of a spherical simplex and the sum of volumes of it and its polar from these formulae for the unit sphere in the odd- and even-dimensional Euclidean spaces, respectively.


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