Document Type

Publication - Article

A Binary-Based Enumeration of the Primitive Pythagorean Triples

Authors

Colton H. Davis, School of Engineering and Physics, Southern Adventist University, Collegedale, TN 37315
Kenneth E. Caviness, Southern Adventist UniversityFollow

Department

Physics & Engineering

Date of Activity

Winter 3-12-2023

Abstract

All primitive Pythagorean triples (PPTs), up to an arbitrarily chosen integer n, are generated by a new binary-based algorithm using the Calkin–Wilf enumeration of the rational numbers. Graphical and tabular displays of the results are provided, including the complete derivation to show the steps from the positive integers n, to a filtered list of "compliant" natural numbers, to (u,v) pairs, to the PPTs of the form (A,B,C). In graph modes, either (A,B) or (u,v) can be displayed, with points identified. Zooming in on the region near the origin shows that this algorithm is not directly connected to the distance from the origin, but it offers hope that such an algorithm might be constructed.

Comments

This was a joint project with a physics major.

Recommended Citation

Colton H. Davis, Kenneth E. Caviness (2023), "A Binary-Based Enumeration of the Primitive Pythagorean Triples" Wolfram Demonstrations Project. demonstrations.wolfram.com/ABinaryBasedEnumerationOfThePrimitivePythagoreanTriples/