TL;DR
The paper introduces the Farey determinants matrix, a new matrix operation that visualizes properties of Farey fractions, enabling intuitive understanding and revealing hierarchical structures within Farey determinants.
Contribution
It presents a novel matrix based on Farey fractions that visualizes properties and reveals hierarchical block structures, aiding comprehension of Farey sequences.
Findings
Matrix visualizes Farey fraction properties
Contains lower order matrices as blocks
Facilitates intuitive demonstrations of theorems
Abstract
A new matrix operation based on inserting columns and rows, similarly to the mediant operation between fractions, gives rise to the Farey determinants matrix or, equivalently, the matrix of the numerators of the differences of Farey fractions. This matrix allows to visualize established properties and theorems of Farey fractions allowing for more intuitive demonstrations and easier understanding. Furthermore it is shown how some Farey determinants matrices contain other lower order Farey determinants matrices as block matrices around the main diagonal.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics and Applications · Analytic Number Theory Research · Advanced Mathematical Theories and Applications