Mathematics > Number Theory
arXiv:2606.24931 (math)
[Submitted on 22 Jun 2026]
Abstract:In this paper, we introduce a matrix-based binary tree that forms the foundation of both the Stern--Brocot and Calkin--Wilf trees. We then explore its connection to continued fractions. Building on this relationship, we provide a path-based representation of Brillhart's proof of the sum of two squares.
Submission history
From: Hongshen Chua [view email]
[v1]
Mon, 22 Jun 2026 08:10:48 UTC (5 KB)
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.


























