TY - JOUR
T1 - Integration bounds for the regular simplex in n-dimensional space
AU - Williams, David M.
AU - Walters, Gage S.
N1 - Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.1080/0020739X.2020.1831090
DO - 10.1080/0020739X.2020.1831090
M3 - Comment/debate
AN - SCOPUS:85092673109
SN - 0020-739X
VL - 52
SP - 1260
EP - 1275
JO - International Journal of Mathematical Education in Science and Technology
JF - International Journal of Mathematical Education in Science and Technology
IS - 8
ER -