A new parameterisation of Pythagorean triples in terms of odd and even series

2015/04/01 by Anthony Overmars, Overmars, Anthony, Lorenzo Ntogramatzidis +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Robotic Mechanisms and Dynamics #math.HO

paper · pdf · doi:10.48550/arxiv.1504.03163

arxiv created 2015/04/01 · openalex publication_date 2015/04/01 · arxiv updated 2015/04/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a formula that parameterises the Pythagorean triples as elements of two series. With respect to the standard Euclidean formula, this parameterisation does not generate the Pythagorean triples where the elements of the triple are all divisible by 2. A necessary and sufficient condition is also proposed for a Pythagorean triple obtained from this formula to be primitive.

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