A recent breakthrough in computer-assisted mathematics showed that every set of 30 points in the plane in general position (i.e., without three on a common line) contains an empty convex hexagon, thus closing a line of research dating back to the 1930s.
Mar 26, 2024
Sep 2, 2024 · In this paper, we formalize and verify this result in the Lean theorem prover. Our formalization covers ideas in discrete computational geometry and SAT ...
Nov 19, 2023 · Heule and Scheucher solved this problem with a combination of geometric insights and automated reasoning techniques by constructing CNF formulas ...
Mar 26, 2024 · Overall, we hope that this work sets a new standard for verification when extensive computation is used for discrete geometry problems, and that ...
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What is the identification of hexagon?
Mar 27, 2024 · Formal verification of the empty hexagon number. ~ Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro ...
The natural way to approach the empty-hexagon problem is to break hexagons into triangles and reason about whether each triangle has a point in its interior.
![PDF] Formally Proving the Boolean Pythagorean Triples Conjecture ...](https://www.google.com/imgres?imgurl=https://figures.semanticscholar.org/22dd81b55397f5d6467c593909175563f6bd6b5d/3-Figure1-1.png&imgrefurl=https://www.semanticscholar.org/paper/Formally-Proving-the-Boolean-Pythagorean-Triples-Cruz-Filipe-Schneider-Kamp/22dd81b55397f5d6467c593909175563f6bd6b5d&h=486&w=1000&tbnid=Iy6I78C_OYdT-M&q=Formal+Verification+of+the+Empty+Hexagon+Number.&tbnh=72&tbnw=149&usg=AI4_-kQbQ9uCR7Hf9EhkQahkKhU8-LggfQ&vet=1&docid=Q3Jplh7QM0QGcM&sa=X&ved=2ahUKEwjPnbrNn9yKAxVmKEQIHQWUOe4Q9QF6BAgMEAg)
Mar 27, 2024 · ... Formal Verification of the Empty Hexagon Number" That is: formally verifying in Lean the "by-hand" encoding step of the recent SAT-solver ...
... Formal Verification of the Empty Hexagon Number. 15th International Conference on Interactive Theorem Proving (ITP 2024), 2024 lean4; Floris Doorn, Heather ...
Oct 31, 2024 · Hitarth gave the research talk. Formal Verification of the Empty Hexagon Number. Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, ...