Campus Units
Mathematics
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
1-25-2021
Journal or Book Title
arXiv
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)=n3/24(1+o(1)). Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Owner
The Authors
Copyright Date
2021
Language
en
File Format
application/pdf
Recommended Citation
Balogh, József; Clemen, Felix Christian; and Lidicky, Bernard, "Maximum Number of Almost Similar Triangles in the Plane" (2021). Mathematics Publications. 264.
https://lib.dr.iastate.edu/math_pubs/264
Comments
This preprint is made available through arXiv: https://arxiv.org/abs/2101.10304.