Primitive Pythagorean Triples 1: Scatter Plot

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration plots primitive Pythagorean triples (PPTs) to make lovely, interesting patterns in the - plane. The details provide definitions to classify all triples that are solutions of the Pythagorean formula in integers. The 2D plot shows integer points that satisfy this equation for some integer .

Contributed by: Robert L. Brown (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Let be a Pythagorean triple (PT), that is, , , and are positive integers such that . A primitive Pythagorean triple (PPT) is a PT with . Redundants are solutions that allow , , and to be negative. This Demonstration illustrates all 16 solutions, and .

PPTs can be given unique base-3 ID numbers. See the Demonstration "Primitive Pythagorean Triples 3: Ordered Tree Graph" for the definitions.

Click "PPT 1" or "PPT 2" to see the subset of PPTs with base-3 ID numbers beginning with 1 or 2.



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