Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T14:21:17.314Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Courant, R. and John, F., Introduction to calculus and analysis, vol. 2, (Wiley, New York, 1974).Google Scholar
[2]Fikhtentol'ts, G. M., The fundamentals of mathematical analysis, Vol. 1, (Pergamon Press, Oxford, 1965).Google Scholar
[3]Joachimsthal, F., ‘Sur quelques applications des déterminants á la géométrie’, J. Reine Angew. Math. von Crelle 40 (1850), 21–47.Google Scholar
[4]Saunders, D., ‘Errors in Navigation’, Math. Spectrum 17 (1982) 4–8.Google Scholar