Generalized perfect parallelograms and their matrix generators

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Abstract
  • Perfect parallelograms have edge lengths and diagonal lengths that are all
    positive integers. These generalize Pythagorean triples which are perfect
    rectangles. We consider the distribution of perfect parallelograms and
    show they satisfy a quadratic Diophantine equation. The solutions to that
    Diophantine equation can be generated by a finite collection of matrices
    that generalizes the matrix based tree of Pythagorean triples.
TitleGeneralized perfect parallelograms and their matrix generators
CreatorSawyer, J. F.
Reiter, Clifford A.
PublisherJP Journal of Algebra, Number Theory and Applications
Academic DepartmentMathematics
DivisionNatural Sciences
OrganizationLafayette College
Date Issued2010
Date Available2011-01-31T14:03:48Z
TypeArticle
LanguageEnglish
Keywordgeneralized Pythagorean triangles
perfect cuboid
Barning tree
perfect parallelepiped
Bibliographic CitationReiter, C. A. and J. F. Sawyer. (2010) "Generalized perfect parallelograms and their matrix generators." JP Journal of Algebra, Number Theory and Applications 16 (1): 1-12
Standard IdentifierHandle 10385/788
Permalinkhttp://hdl.handle.net/10385/788
Rights Statement In Copyright In Copyright
Rights HoldersPushpa Publishing House
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