Integration bounds for the regular simplex in n-dimensional space

Abstract

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.

Keywords:

• Regular simplex
• equilateral triangle
• regular tetrahedron
• integration bounds

AMS CLASSIFICATIONS:

• 52B11
• 51M25
• 26B15
• 65-02

Disclosure statement

No potential conflict of interest was reported by the authors.