SPHERICAL SIMPLICES AND THEIR POLARS |
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| Authors: | Sato Kenzi |
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| Institution: | Department of Mathematics, Faculty of Engineering, Tamagawa University, 6-1-1, Tamagawa-Gakuen, Machida, Tokyo 194-8610, Japan |
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| Abstract: | This article is about spherical simplices in the unit sphere.One of the purposes is to give a relation of dihedral anglesof a spherical simplex and its polar, and the other is to givetwo simple formulae of volumes of spherical simplices and theirpolars. We can calculate the volume of a spherical simplex andthe sum of volumes of it and its polar from these formulae forthe unit sphere in the odd- and even-dimensional Euclidean spaces,respectively. |
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