Skip to main content Accessibility help
×
Home

The volumes of simplices, or, find the penguin

  • Fima C. Klebaner (a1), Aidan Sudbury (a1) and G. A. Watterson (a1)

Abstract

Given the equations for the n + 1 hyperplanes that bound an n-simplex in Rn, simple formulae are derived for the contents of the nr 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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The volumes of simplices, or, find the penguin
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      The volumes of simplices, or, find the penguin
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      The volumes of simplices, or, find the penguin
      Available formats
      ×

Copyright

References

Hide All
[1]Courant, R. and John, F., Introduction to calculus and analysis, vol. 2, (Wiley, New York, 1974).
[2]Fikhtentol'ts, G. M., The fundamentals of mathematical analysis, Vol. 1, (Pergamon Press, Oxford, 1965).
[3]Joachimsthal, F., ‘Sur quelques applications des déterminants á la géométrie’, J. Reine Angew. Math. von Crelle 40 (1850), 2147.
[4]Saunders, D., ‘Errors in Navigation’, Math. Spectrum 17 (1982) 48.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

Related content

Powered by UNSILO

The volumes of simplices, or, find the penguin

  • Fima C. Klebaner (a1), Aidan Sudbury (a1) and G. A. Watterson (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.