Metric properties in Berggren tree of primitive Pythagorean triples

2023/04/11 by Lucia Janičková, Janičková, Lucia, Evelin Csókási +1
Mathematics · Engineering · #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2304.05230

Abstract

A Pythagorean triple is a triple of positive integers (x,y,z) such that x²+y²=z². If x,y are coprime and x is odd, then it is called a primitive Pythagorean triple. Berggren showed that every primitive Pythagorean triple can be generated from triple (3,4,5) using multiplication by uniquely number and order of three 3×3 matrices, which yields a ternary tree of triplets. In this paper, we present some metric properties of triples in Berggren tree. Firstly, we consider primitive Pythagorean triple as lengths of sides of right triangles and secondly, we consider them as coordinates of points in three-dimensional space.

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