The Modular Tree of Pythagorus
History and Overview
2007-05-23 v1
Authors:
Roger C. Alperin
Abstract
The Pythagorean triples have the structure of a ternary rooted tree; the tree is based on the Cayley graph of a free subgroup of the modular group
Cite
@article{arxiv.math/0010281,
title = {The Modular Tree of Pythagorus},
author = {Roger C. Alperin},
journal= {arXiv preprint arXiv:math/0010281},
year = {2007}
}
Related papers
View all related →
Number Theory · Mathematics
Metric properties in Berggren tree of primitive Pythagorean triples
Lucia Janičková, Evelin Csókási
2023-04-12
Number Theory · Mathematics
Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers
Amnon Yekutieli
2022-01-11
Number Theory · Mathematics
Constructive representation of primitive Pythagorean triples
Natalia Aleshkevich
2021-08-17
History and Overview · Mathematics
A note on Pythagorean Triples
Roberto Amato
2023-05-24
General Mathematics · Mathematics
Construction of primitive Pythagorean triples and Pythagorean triples with a common multiplier using gnomons
Natalia Aleshkevich
2022-05-13
Number Theory · Mathematics
Groups and monoids of Pythagorean triples connected to conics
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru
2017-12-27
History and Overview · Mathematics
A review of Pythagorean triples from both classical and modern viewpoints
Ali Taghavi
2024-06-06
General Mathematics · Mathematics
A simple method for generating rational triangles
Konstantine Zelator
2008-07-08
Number Theory · Mathematics
Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples
Thomas Jaklitsch, Thomas C. Martinez, Steven J. Miller, Sagnik Mukherjee
2021-12-08
General Mathematics · Mathematics
Certain Properties of Pythagorean Triangles involving the interior diameter, and the exterior diameters
Konstantine "Hermes" Zelator
2008-03-26
Combinatorics · Mathematics
On graphs whose Hosoya indices are primitive Pythagorean triples
Tomoe Kadoi, Yasuhide Numata
2014-02-07
Number Theory · Mathematics
The Origin of the Beauregard--Suryanarayan Product on Pythagorean Triples
Shaul Zemel
2020-08-13
Number Theory · Mathematics
Numeric Palindromes in Primitive and Non-primitive Pythagorean Triples
John Rafael M. Antalan, Richard P. Tagle
2015-08-11
Number Theory · Mathematics
Triangular modular curves of low genus
Juanita Duque-Rosero, John Voight
2022-10-03
Combinatorics · Mathematics
Simplicial and Cellular Trees
Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
2015-06-24
General Mathematics · Mathematics
Building the Butterfly Fractal: The Eightfold Way
Indubala I Satija
2024-06-04
Number Theory · Mathematics
A polynomial analogue of Berggren's theorem on Pythagorean triples
Byungchul Cha, Ricardo Conceição
2023-10-04
Combinatorics · Mathematics
Tree sets
Reinhard Diestel
2017-02-28
Combinatorics · Mathematics
Moduli Spaces of Pentagonal Subdivision Tilings
Jinjin Liang, Erxiao Wang, Min Yan
2024-04-19
Number Theory · Mathematics
A Direct Method To Generate Pythagorean Triples And Its Generalization To Pythagorean Quadruples And n-tuples
Tanay Roy, Farjana Jaishmin Sonia
2012-01-11
Combinatorics · Mathematics
A tanglegram Kuratowski theorem
Eva Czabarka, Laszlo A. Szekely, Stephan Wagner
2017-08-02
Rings and Algebras · Mathematics
On the structures of split Leibniz triple systems
Yan Cao, Liangyun Chen
2015-09-17
Combinatorics · Mathematics
The Polyhedral Tree Complex
Michael Dougherty
2024-09-17
Combinatorics · Mathematics
Non-crossing trees, quadrangular dissections, ternary trees, and duality preserving bijections
Nikos Apostolakis
2021-05-05
History and Overview · Mathematics
New relations for the old triangle
Boris Safin
2013-05-06