Heilbronn Triangles in the Unit Square

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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


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