Integration bounds for the regular simplex in n-dimensional space

• David M. Williams ^[1] ; Gage S. Walters ^[1]
  1. [1] Pennsylvania State University

     Pennsylvania State University

     Borough of State College, Estados Unidos

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 52, Nº. 8, 2021, págs. 1260-1275
• Idioma: inglés
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• Resumen

  • 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.