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Eduourd Zeckendorf was an amateur mathematician whose name is given to the property that every positive integer can be represented uniquely as the sum of non-consecutive Fibonacci numbers, the sequence defined by
F1 = F2 = 1 and Fn = Fn-1 + Fn-2 for n > 2.
This is called Zeckendorf's theorem, and the subsequence of Fibonacci numbers which add up to a given integer is called its Zeckendorf representation. (Because F1= F2, we need to exclude F1 from the representation to give uniqueness.) For example,
71 = 55 + 13 + 3,
1111 = 987 + 89 + 34 + 1.
Zeckendorf qualified as a medical doctor, became an officer in the Belgium army in 1925 and subsequently also qualified as a dentist. Following the surrender of the Belgium army in May 1940 Zeckendorf was interned as a prisoner of war until 1945. He subsequently published several mathematical papers, nearly all of them in the Bulletin de la Société Royale des Sciences de Liège, mainly on elementary number theory.
Article by: G M Phillips, St Andrews
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