Integration bounds for the regular simplex in n-dimensional space

David M. Williams, Gage S. Walters

Research output: Contribution to journalComment/debatepeer-review


The purpose of this article is to provide an explicit formula for the bounds of integration of the regular simplex centred at the origin. Furthermore, this article rigorously proves that these integration bounds recover the volume of the regular simplex. To the authors' knowledge, this is the first time that such integration bounds have been explicitly formulated in the mainstream literature. In addition, the derivation of the simplex volume using integration bounds appears to be new. As a result, this article has the potential to serve as a useful resource for a broad audience, including teachers of mathematics, engineers, and recreational geometers.

Original languageEnglish (US)
Pages (from-to)1260-1275
Number of pages16
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number8
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


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