Name
Abstract | ||
|---|---|---|
A triangle T' is epsilon-similar to another triangle T if their angles pairwise differ by at most epsilon. Given a triangle T, epsilon > 0 and n is an element of & nbsp;N, Barany and Furedi asked to determine the maximum number of triangles h(n, T, epsilon) being epsilon-similar to T in a planar point set of size n. We show that for almost all triangles T there exists epsilon = epsilon(T) > 0 such that h(n, T, epsilon) = (1 + o(1))n3/24. Exploring connections to hypergraph Turan problems, we use flag algebras and stability techniques for the proof. (C)& nbsp;2022 Published by Elsevier B.V. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.comgeo.2022.101880 | COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS |
Keywords | DocType | Volume |
Similar triangles, Extremal hypergraphs, Flag algebras | Journal | 105 |
ISSN | Citations | PageRank |
0925-7721 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| József Balogh | 1 | 0 | 1.35 |
| Felix Christian Clemen | 2 | 0 | 2.03 |
| Bernard Lidický | 3 | 0 | 1.01 |