Affiliation:
1. University Al. I. Cuza, Iasi
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.
Publisher
Mathematical Sciences and Applications E-Notes
Reference9 articles.
1. [1] Kramer, Jürg., Pippich, A. M. V.: Snapshots of modern mathematics from Oberwolfach: Special values of zeta functions and areas of triangles. Notices of American Mathematical Society, 63(8), 917-922 (2016).
2. [2] Bonahon, F.: Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots. American Mathematical Society; Princeton, NJ: Institute for Advanced Study. 2009.
3. [3] Katok, S., Ugarcovici I.: Symbolic dynamics for the modular surface and beyond. Bulletin of American Mathematical Society, New Ser. 44(1), 87-132 (2007).
4. [4] Hatcher, A.: Topology of Numbers. American Mathematical Society. 2022.
5. [5] Jitman, S., Sangwisut, E.: The group of primitive Pythagorean triples and perplex numbers. Mathematics Magazine. 95(4), 285-293 (2022).