Zeckendorf's Theorem/Historical Note
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Historical Note on Zeckendorf's Theorem
Zeckendorf's Theorem appears to have been discovered in medieval India.
Edouard Zeckendorf rediscovered it in $1939$, but did not actually publish it until $1972$.
Cornelis Gerrit Lekkerkerker had in fact published it in $1952$, and named it after Zeckendorf at that time.
By the time Zeckendorf published his summary of this result in $1972$ several others had been referring to it as Zeckendorf's Theorem as a result of Lekkerkerker's article.
It is in fact a special case of a theorem by Alexander Markowich Ostrowski which had been published in $1922$.
Sources
- 1922: Alexander Ostrowski: Bemerkungen zur Theorie der diophantischen Approximationen (Abh. Math. Semin. Univ. Hambg. Vol. 1: pp. 77 – 98)
- 1922: Alexander Ostrowski: Zu meiner Note: "Bemerkungen zur Theorie der Diophantischen Approximationen" im l.Heft dieses Bandes (Abh. Math. Semin. Univ. Hambg. Vol. 1: pp. 249 – 250)
- 1952: C.G. Lekkerkerker: Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci (Simon Stevin Vol. 29: pp. 190 – 195)
- 1972: E. Zeckendorf: Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas (Bull. Soc. R. Sci. Liège Vol. 41: pp. 179 – 182)