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A Geometrical Way to Sum Powers by Means of Tetrahedrons and Eulerian Numbers

2011/03/21 by Mario Barra, Barra, Mario
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #math.HO

paper · pdf · doi:10.48550/arxiv.1103.4288

12 pages, based on lecture notes to undergraduaded students

arxiv created 2011/03/21 · openalex publication_date 2011/03/21 · arxiv updated 2011/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the sums of the tetrahedrons, whose calculation is trivial.

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