Pythagorean Triples: Visualization Using Complex Numbers and Applications

Abstract

This paper examines the nature of Pythagorean triples and how complex numbers can be used to generate, as well as, visualize Pythagorean triples. The information in this paper is formatted in a way to take the reader on a journey through Pythagorean triples, exploring all its dimensions in order to gain a deeper understanding of the subject. We start at the beginning by defining what exactly complex numbers are, then move forward into methods of how we can generate Pythagorean triples and primitive Pythagorean triples. By combining both of these sections, we gain a deeper understanding of these triples and use this knowledge to visualize them. Furthermore, this paper presents proofs and applications to help display the level of understanding we intend to gain by formatting the paper as such. We start from the very beginning, then use what is learned along the way to help further the understanding of Pythagorean triples.