Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Square Representation of Farey Sequences

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The Farey sequence of order runs over all the irreducible rational numbers between 0 and 1 with denominator at most , constructed by the Farey addition of consecutive pairs of terms from the previous Farey sequence. The Farey addition of two given fractions and is defined as .

[more]

The diagram is based on the result that, if we construct a quadrilateral with vertices , , and , then the diagonal lines of this figure intersect at the point .

[less]

Contributed by: Carlos Enrique Nosa Guzman (August 2022)
Open content licensed under CC BY-NC-SA

Snapshots

Details

This Demonstration is based on [1, Chapter 1].

Reference

[1] A. Hatcher, Topology of Numbers, New York: Cornell University, 2018.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send