Symmetry-Based Approach to the Problem of a Perfect Cuboid

被引：0
|
作者：
Sharipov R.A. [1 ]
机构：
[1] Bashkir State University, Ufa
来源：
Journal of Mathematical Sciences | 2021年 / 252卷 / 2期
关键词：
11D09; 11D41; 11D72; Diophantine equation; perfect cuboid; polynomial;
D O I：
10.1007/s10958-020-05159-4
中图分类号：
学科分类号：
摘要：
A perfect cuboid is a rectangular parallelepiped in which the lengths of all edges, the lengths of all face diagonals, and also the lengths of spatial diagonals are integers. No such cuboid has yet been found, but their nonexistence has also not been proved. The problem of a perfect cuboid is among unsolved mathematical problems. The problem has a natural S3-symmetry connected to permutations of edges of the cuboid and the corresponding permutations of face diagonals. In this paper, we give a survey of author’s results and results of J. R. Ramsden on using the S3 symmetry for the reduction and analysis of the Diophantine equations for a perfect cuboid. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
页码：266 / 282
页数：16
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