Hugo Hadwiger’s influence on geometric dissections with special properties

On the occasion of the Swiss Mathematical Society’s centennial, it is both an honor and a pleasure to contribute an article to this special edition of the Elemente der Mathematik on a mathematical subject from the work of Hugo Hadwiger. Professor Hadwiger was a prolific and influential Swiss mathematician known for his work in geometry, combinatorics, and cryptography [2]. Here we shall note how his ideas in dissection geometry have been extended into the present. The focus will proceed from his article, “Zerlegungsgleichheit ebener Polygone” [13], co-authored with Paul Glur, which appears to be the most-referenced of his articles on dissection. In the almost sixty years since this article appeared, several popular books on geometric dissections [4, 5, 6, 15] have been published, a superb website [17] has been created, and an early manuscript [12] has been recovered.