Encounters with Paul Erdős
My first encounter with Paul Erdős was curiously indirect. As a pre-undergraduate at Cambridge (England) in 1934, I learned from one of the Trinity College tutors that a mathematician named Erdős, passing through Cambridge, had mentioned an intriguing conjecture (attributed to Lusin, I believe), implying that a square could not be dissected into a finite number of unequal smaller square pieces. I passed this problem on to three fellow-students, and we eventually found methods that produced counterexamples (). Of recent years the advent of high-speed computing has given rise to a considerable industry listing large numbers of dissections of squares into unequal squares ( and  for example), an industry that could continue indefinitely as there are infinitely many different dissections of this kind.
Unable to display preview. Download preview PDF.
- C.J. Bouwkamp and A. J. W. Duijvestijn, Catalogue of Simple Perfect Squared Squares of orders 21 through 25, Eindhoven University of Technology 1992.Google Scholar
- Jasper Dale Skinner II, Squared Squares: Who’s Who and What’s What, Lincoln, Nebraska, 1993.Google Scholar
- C. Engelman, On close-packed double-error-correcting codes on p symbols, I. R. E. Transactions on Information Theory, Correspondence, January 1961, 51–52.Google Scholar
- V. A. Lebesgue, Sur l’impossibilité en nombres entiers de 1’ équation xm = y2-bl, Nouv. Ann. Math. 9 (1850), 178–181.Google Scholar