The Classical Rational Cuboid Table of Maurice Kraitchik.

Rathbun, Randall L.; Granlund, Torbjörn

doi:10.2307/2153431

Cited by 4 publications

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“…If the parallelogram face becomes a rectangle, then we have a standing box. Computer aided discoveries have shown the existence of perfect leaning boxes [3,4,5]. We found a two-parameter family of solutions for rational leaning boxes analytically.…”

Section: Introductionmentioning

confidence: 79%

No Perfect Cuboid

Wyss¹

2015

Preprint

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Section: Introductionmentioning

confidence: 79%

No Perfect Cuboid

Wyss¹

2015

Preprint

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“…Manual searches have been done, Maurice Kraitchik's Rational Cuboid Table [5,6,7] is a classic example which took thousands of hours to produce. His table has been corrected and expanded with the help of a computer [8]. So we will enlist the aid of a computer to help in expediting that search process.…”

Section: Setting Up the Pythagorean Group P Y(n)mentioning

confidence: 99%

The Integer Cuboid Table

Rathbun

2017

Preprint

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Integer cuboids are rectangular Diophantine parallelepipeds It has been discovered that these cuboids come in 3 varieties: Euler or body type, edge type, and face type. In all three cases, one edge or diagonal is irrational, all others are rational. We discuss an exhaustive computer search procedure which uses the Pythagorean group P y(n) to locate all possible cuboids with a given edge n. Over the range of 44 to 1.76 • 10 11 , for the smallest edge, 160,594 cuboids were discovered. They are listed in the Integer Cuboid Table .

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“…a, b, c, d ab , d bc , d ac , d s only one face diagonal or side is irrational, then this is called nearly-perfect cuboid (NPC). Numerous EC and NPC have been found by the help of computers [1][2][3][4][5][6][7]. As for the search for a PC, the computer programs of many researchers in many countries have been unsuccessful.…”

Section: Introductionmentioning

confidence: 99%

Perfect Cuboid and Congruent Number Equation Solutions

Meskhishvili

2012

Preprint

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A perfect cuboid (PC) is a rectangular parallelepiped with rational sides a, b, c whose face diagonals d ab , d bc , d ac and space (body) diagonal d s are rationals. The existence or otherwise of PC is a problem known since at least the time of Leonhard Euler. This research establishes equivalent conditions of PC by nontrivial rational solutions (X, Y ) and (Z, W ) of congruent number equationwhere product XZ is a square. By using such pair of solutions five parametrizations of nearly-perfect cuboid (NPC) (only one face diagonal is irrational) and five equivalent conditions for PC were found. Each parametrization gives all possible NPC. For example, by using one of them -invariant parametrization for sides and diagonals of NPC are obtained:Because each parametrization is complete, inverse problem is discussed. For given NPC is found corresponding congruent number equation (i.e. congruent number) and its solutions.

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The Classical Rational Cuboid Table of Maurice Kraitchik.

Cited by 4 publications

References 0 publications

No Perfect Cuboid

No Perfect Cuboid

The Integer Cuboid Table

Perfect Cuboid and Congruent Number Equation Solutions

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