JP Journal of Algebra, Number Theory and Applications
Volume 6, Issue 2, Pages 279 - 294
(August 2006)
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PURSUING THE PERFECT PARALLELEPIPED
Clifford A. Reiter (U. S. A.) and Jordan O. Tirrell (U. S. A.)
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Abstract: Whether there exists a parallelepiped with edges, face diagonals, and main diagonals all of integer length is an open question. This is equivalent to thirteen linked quadratic diophantine equations. We look at the basic diophantine equation: the structure of integer length vectors in dimensions two, three, and four and give matrix generators for producing all the 3-dimensional integer length integer vectors. Parametric families of parallelepipeds that have good properties and the results of computer searches for perfect parallelepipeds are also described. |
Keywords and phrases: perfect parallelepiped, perfect cuboid. |
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