Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

The Lonely Runner Conjecture

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.

There are runners going around a circular track of unit length. They all start together from the same spot and each one has their own distinct speed. The distance between two runners is the distance around the track between them. A runner is defined as lonely if his distance to any other runner is at least .

[more]

The Lonely Runner conjecture states that each runner becomes lonely at some time [1]. The conjecture has been proven for up to seven runners [2].

This Demonstration lets you verify this conjecture. Select a number of runners and start the race. When a runner becomes lonely, his position and his marker on the speed gauge turn red and two red arcs of length are displayed fore and aft of his position.

Each new race or renewed selection of the number of runners generates a different set of random speeds.

[less]

Contributed by: Erik Mahieu (May 2014)
Open content licensed under CC BY-NC-SA

Snapshots

Details

References

[1] T. S. Roberts. "Lonely Runner Conjecture." Unsolved Problems in Number Theory, Logic, and Cryptography. (May 21, 2014) unsolvedproblems.org/index_files/LonelyRunner.htm.

[2] S. Czerwiński, "Random Runners Are Very Lonely." arxiv.org/pdf/1102.4464.pdf.

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