PROOF OF THE IMPOSSIBILITY OF THE PERFECT CUBOID EXISTENCE
DOI:
https://doi.org/10.31618/ESSA.2782-1994.2021.1.70.70Keywords:
Euler parallelepideds, perfect cuboid, spatial diagonal, cube doubling problem, irrationalityAbstract
The problem of finding, among the Euler parallelepipeds, one with an integer spatial diagonal, called the perfect cuboid problem, is one of the unsolved mathematical problems from the section of number theory. This article provides mathematical proof of the impossibility of the existence of the perfect cuboide among all possible Euler parallelepipeds. A mathematical justification for an equivalence of the problem of doubling a cube and the problem of constructing a perfect cuboid is also given.
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