Wolfram Demonstrations Project

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

Visible Lattice Points and Approximations to Pi

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.

A lattice point is visible from the origin if there is no other lattice point on the segment , which happens if and only if . The proportion of such lattice points is .

[more]

This Demonstration uses that fact to approximate π. The blue points represent the lattice points that are visible from the origin, and the red points those that are not visible. The pitch of the sound is proportional to the GCD of the current point.

[less]

Contributed by: Chingis Matayev (August 2015)
(Illinois Mathematics Summer REU Program 2015)
Open content licensed under CC BY-NC-SA

Snapshots

Details

detailSectionParagraph
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