Year: 2015
Type: preprint
Abstract: Meskhishvili provided three rational parametrizations for nearly perfect cuboids where one face diagonal remains unresolved. This paper analyzes his second and third parametrizations and proves that the two fundamental infinite subfamilies of the associated Pell equation cannot resolve the remaining diagonal to form a non-degenerate perfect cuboid. Consequently, these specific subfamilies can be safely excluded from future computational searches. Furthermore, a definitive, explicitly testable exclusion corridor is established for the third family. All proofs rely entirely on exact polynomial identities and strict integer inequalities, avoiding any asymptotic approximations.
Source: arXiv (Cornell University)
Author: Meskhishvili, Mamuka
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W39093033