No Perfect Cuboid

2015/06/07 by Walter Wyss, Wyss, Walter · 1 citation
Engineering · Mathematics · #11Dxx #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems #math.NT #msc:11Dxx

paper · pdf · doi:10.48550/arxiv.1506.02215

openalex publication_date 2015/06/07 · arxiv created 2017/05/17 · arxiv updated 2017/05/18 · openalex created_date 2023/03/08 · openalex updated_date 2026/07/28

Abstract

A rectangular parallelepiped is called a cuboid (standing box). It is called perfect if its edges, face diagonals and body diagonal all have integer length. Euler gave an example where only the body diagonal failed to be an integer (Euler brick). Are there perfect cuboids? We prove that there is no perfect cuboid.

Cited by

• On Walter Wyss's no perfect cuboid paper

Related

• The Non-existence of Perfect Cuboid
• Perfect cuboid, primitive Pythagorean triples and Eulerian parallelepipeds. Dynamics of construction
• There is no Perfect Cuboid
• On Walter Wyss's no perfect cuboid paper
• On the equivalence of cuboid equations and their factor equations