TL;DR
This paper proves a conjecture related to the geometry of triangles, specifically showing that no acute rational-angled triangle possesses the lattice property, advancing understanding in mathematical billiards and geometric structures.
Contribution
It establishes the nonexistence of acute rational-angled triangles with the lattice property, resolving a conjecture by Kenyon and Smillie.
Findings
No acute rational-angled triangle has the lattice property
Confirmed the conjecture of Kenyon and Smillie
Advances understanding of billiard dynamics in polygons
Abstract
We prove a conjecture of Kenyon and Smillie concerning the nonexistence of acute rational-angled triangles with the lattice property.
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