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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Notes
- 1.
P. Erdős remarks: autumn 1939
- 2.
P. Erdős remarks: 1943
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Stone, A.H. (2013). Encounters with Paul Erdős. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_6
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