Novel required properties of, and efficient algorithms to seek, perfect cuboids

Fuente: arXiv
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Main Authors: de Grey, Aubrey, Gibbs, Philip, Helm, Louie
Format: Preprint
Published: 2024
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author de Grey, Aubrey
Gibbs, Philip
Helm, Louie
author_facet de Grey, Aubrey
Gibbs, Philip
Helm, Louie
contents We present a novel approach to the age-old question of whether perfect cuboids exist. Our approach consists of two new computer search algorithms, arising from the analysis of "perfect plinths" reported by one of us recently, that are much more efficient than any prior algorithm of which we are aware. Using this approach, we also (i) identify some new two-parameter families of edge cuboids, and (ii) show that large proportions of aspect ratios of faces or internal rectangles cannot be present in a perfect cuboid, a property that was previously reported only for faces with the aspect ratio 4:3.
format Preprint
id arxiv_https___arxiv_org_abs_2401_06784
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Novel required properties of, and efficient algorithms to seek, perfect cuboids
de Grey, Aubrey
Gibbs, Philip
Helm, Louie
General Mathematics
11D99
We present a novel approach to the age-old question of whether perfect cuboids exist. Our approach consists of two new computer search algorithms, arising from the analysis of "perfect plinths" reported by one of us recently, that are much more efficient than any prior algorithm of which we are aware. Using this approach, we also (i) identify some new two-parameter families of edge cuboids, and (ii) show that large proportions of aspect ratios of faces or internal rectangles cannot be present in a perfect cuboid, a property that was previously reported only for faces with the aspect ratio 4:3.
title Novel required properties of, and efficient algorithms to seek, perfect cuboids
topic General Mathematics
11D99
url https://arxiv.org/abs/2401.06784