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Encounters with Paul Erdős

In: The Mathematics of Paul Erdős I

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  • Arthur H. Stone

    (Northeastern University, Department of Mathematics)

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.

Suggested Citation

  • Arthur H. Stone, 2013. "Encounters with Paul Erdős," Springer Books, in: Ronald L. Graham & Jaroslav Nešetřil & Steve Butler (ed.), The Mathematics of Paul Erdős I, edition 2, pages 93-98, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7258-2_6
    DOI: 10.1007/978-1-4614-7258-2_6
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