A Note on a Very Simple Property About the Volume of a n-Simplex and the Centroids of its Faces

  1. González-Santander Martínez, Juan Luis
  2. Martín González, Germán
Revue:
Nereis: revista iberoamericana interdisciplinar de métodos, modelización y simulación

ISSN: 1888-8550

Année de publication: 2015

Número: 7

Pages: 51-58

Type: Article

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Résumé

A n–simplex is the convex hull of a set of (n + 1) independent points affine to a n–dimensional Euclidean space. A 0–simplex would be a point, a segment would be a 1–simplex, a 2–simplex would be a triangle and a 3–simplex a tetrahedron. If we connect to each other the centroids of all the (n − 1) faces of a n–simplex, we will obtain another n-simplex (dual n-simplex). The volume ratio between a n-simplex and its dual is just n−n.

Références bibliographiques

  • Eric W. Weisstein, Medial Triangle. From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/MedialTriangle.html.
  • P. Stein, A Note on the Volume of a Simplex. American Mathematical Monthly 73 (1966) 299–301.
  • Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze attinenti la meccanica e i movimenti locali, 1638. Available at http://galileoandeinstein.physics.virginia.edu/
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