Gaussian propeller — the best partition of space (3D)

About this app

A Gaussian hill, glass walls that split it into sectors, and arrows for the Gaussian centroids of the cells: drag the walls, 2 to 6 sectors, shift the centre, compare half-space, tetrahedron, cube and octants in space. The measuring ring closes only for the propeller of three 120° sectors with value 9/(8π). Result from openai/math (family 096, formalised in Lean): no partition in any dimension gets above it. Exhibit-ready.

Subject: Open problems, solved by AI

More from Open problems, solved by AI

• Anderson localisation: 2D vs. 3D (3D)
• Barnette's conjecture: a round trip over every polyhedron (3D)
• Cardy's formula — percolation in a random tiling
• The plane is not five-colourable (Hadwiger–Nelson)
• Triangular billiards — irrational angles mix (3D)
• Triangular lattice — universal optimality
• First-passage percolation
• Gaussian moat — no path to infinity

A VisuApp by heyprof: interactive, free in your browser, no sign-up. What is a VisuApp? · All apps