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

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.

💡 Research Summary

The paper presents a novel geometric framework for evaluating power sums, traditionally expressed as (\sum_{k=1}^{n} k^{p}). The author begins by recalling the classical Faulhaber formulas, which rely on Bernoulli numbers and often involve cumbersome algebraic manipulations. Seeking a more intuitive approach, the study shifts focus to a d‑dimensional hypercube (