Heilbronn Triangles in the Unit Square

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.

For points in a square of side length one, find the three points that make the triangle with minimal area. Finding the placement of points that produces the largest such triangle is known as the Heilbronn triangle problem. The point placements within this Demonstration are the best known. Minimal triangles are colored red. All solutions above 12 points are due to Mark Beyleveld and David Cantrell, with optimization and exact solutions found by Mathematica.

Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA




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.