The Number of Unit-Area Triangles in the Plane: Theme and Variation

Orit E. Raz*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We show that the number of unit-area triangles determined by a set S of n points in the plane is O(n20/9), improving the earlier bound O(n9/4) of Apfelbaum and Sharir [2]. We also show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles that S spans can be Ω(n2), for any triple of lines (it is always O(n2) in this case).

Original languageAmerican English
Pages (from-to)1221-1240
Number of pages20
JournalCombinatorica
Volume37
Issue number6
DOIs
StatePublished - 1 Dec 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.

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