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The volumes of simplices, or, find the penguin

Part of: Projective and enumerative geometry

Published online by Cambridge University Press:  09 April 2009

Fima C. Klebaner ,
Aidan Sudbury  and
G. A. Watterson
Fima C. Klebaner
Affiliation:
Department of Mathematics, Monash University Clayton, Victoria 3168, Australia
Aidan Sudbury
Affiliation:
Department of Mathematics, Monash University Clayton, Victoria 3168, Australia
G. A. Watterson
Affiliation:
Department of Mathematics, Monash University Clayton, Victoria 3168, Australia
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Abstract

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Given the equations for the n + 1 hyperplanes that bound an n-simplex in Rn, simple formulae are derived for the contents of the n − r simplices (0 ≦ r < n) embedded in it. For example, when n = 3, the formulae include the volume of the tetrahedron, the areas of its faces and the lengths of its edges.

Keywords

simplexvolume.

MSC classification

Secondary: 14N99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 263 - 268
Copyright
Copyright © Australian Mathematical Society 1989

References

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