Further generalizations of the parallelogram law

  • Antonio M. Oller-Marcén Centro Universitario de la Defensa de Zaragoza

Abstract

In a recent work of Alessandro Fonda, a generalization of the parallelogram law in any dimension $N\geq 2$ was given by considering the ratio of the quadratic mean of the measures of the $(N-1)$-dimensional diagonals to the quadratic mean of the measures of the faces of a parallelotope. In this paper, we provide a further generalization considering not only $(N-1)$-dimensional diagonals and faces, but the $k$-dimensional ones for every $1\leq k\leq N-1$.

Published
2020-07-30
Section
Articles