The Mathematics of Paul Erdös I pp 68-73 | Cite as

# Encounters with Paul Erdős

## Abstract

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 ([1]). 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 ([2] and [6] for example), an industry that could continue indefinitely as there are infinitely many different dissections of this kind.

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## References

- E. L. Brooks, C. A. B. Smith, A. H. Stone and W. T. Tutte, The dissection of rectangles into squares, Duke Math. J.
**7**(1940) 312–340.MathSciNetCrossRefGoogle Scholar - 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
- P. Erdôs and A. H. Stone, Some remarks on almost periodic transformations, Bull. Amer. Math. Soc.
**51**(1945) 126–130.MathSciNetCrossRefGoogle Scholar - P. Erdôs and A. H. Stone, On the structure of linear graphs, Bull. Amer. Math. Soc.
**52**(1946) 1087–1091.MathSciNetCrossRefGoogle Scholar - P. Erdôs and A. H. Stone, On the sum of two Borel sets, Proc. Amer. Math. Soc.
**25**(1970) 304–306.MathSciNetGoogle 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 x
^{m}= y^{2}-bl, Nouv. Ann. Math.**9**(1850), 178–181.Google Scholar - L. J. Mordell, Diophantine Equations, Academic Press 1969, esp. p. 301.MATHGoogle Scholar
- I. Niven and H. S. Zuckerman, Introduction to the Theory of Numbers, Wiley, New York 1960.MATHGoogle Scholar