A Note on a Very Simple Property About the Volume of a n-Simplex and the Centroids of its Faces
- González-Santander Martínez, Juan Luis
- Martín González, Germán
ISSN: 1888-8550
Any de publicació: 2015
Número: 7
Pàgines: 51-58
Tipus: Article
Altres publicacions en: Nereis: revista iberoamericana interdisciplinar de métodos, modelización y simulación
Resum
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.
Referències bibliogràfiques
- 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/