Abstract
A triangle T′ is ε-similar to another triangle T if their angles pairwise differ by at most ε. Given a triangle T, ε>0 and n∈N, Bárány and Füredi asked to determine the maximum number of triangles h(n,T,ε) being ε-similar to T in a planar point set of size n. We show that for almost all triangles T there exists ε=ε(T)>0 such that h(n,T,ε)=(1+o(1))n3/24. Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof.
Original language | English (US) |
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Article number | 101880 |
Journal | Computational Geometry: Theory and Applications |
Volume | 105-106 |
DOIs | |
State | Published - Aug 1 2022 |
Keywords
- Extremal hypergraphs
- Flag algebras
- Similar triangles
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics