The Farey Sum of Pythagorean and Eisenstein Triples
Abstract
A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.
Keywords
Farey sum, Pythagorean (Eisenstein) triple, Symmetric matrix
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