Introduction

Abstract

Erdős’ love for geometry and elementary or discrete geometry in particular, dates back to his beginnings. The Erdős-Szekeres paper has been influential and certainly helped to create discrete geometry as we know it today. But Erdős also put geometry to the service to other branches, giving definition to various geometrical graphs and proving bounds on their chromatic and independence numbers. We are happy to include papers by Moshe Rosenfeld, Pavel Valtr, Janos Pach, Jiří Matoušek and, in particular, a paper by Miklós Laczkovich and Imre Ruzsa on the number of homothetic sets. While the paper of Peter Fishburn is closely related to Erdős’ favorite theme, the papers of N. G. de Bruijn (on Penrose tiling) and J. Aczél and L. Losonczi (on functional equations) cover broader related aspects. It is perhaps fitting to complement this introduction by a few related Erdős problems in his own words:Let x1, …, x n be n points in the plane, not all on a line, and join every two of them. Thus we get at least n distinct lines. This follows from Gallai-Sylvester but also from a theorem of de Bruijn and myself.