Year: 2025
Type: article
Abstract: Paul Erdős posed the question of whether every measurable planar set of infinite Lebesgue measure contains the four vertices of an isosceles trapezoid of unit area. In this paper, we provide an affirmative answer to this question. Additionally, we present affirmative solutions to similar questions by Erdős concerning isosceles triangles and right-angled triangles.
DOI: 10.1090/proc/17322
Author: Junnosuke Koizumi
Institution: RIKEN
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413816454