The Wythoff and the Zeckendorf Representations of Numbers are Equivalent

Wolfdieter Lang

A chapter in Applications of Fibonacci Numbers, 1996, pp 321-337 from Springer

Abstract: Abstract The quintessence of many application of Fibonacci numbers is the binary substitution sequence 1→10, 0→1. The infinite sequence generated this way is self-similar and quasiperiodic. See refs. [7, 16] for details on this rabbit or golden sequences. It is intimately related to Wythoffs complementary sequences which cover the natural numbers ([·] is the greatest integer function) 1 $$ A(m): = \left\lfloor {m\varphi } \right\rfloor ,\,B(m): = \left\lfloor {m{\varphi ^2}}\right\rfloor ,\,m \in \,N,{\varphi ^2} = \varphi + 1,\,\varphi > 0. $$

Keywords: Golden Section; Edge Label; Fibonacci Number; Lucas Number; Golden Sequence (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0223-7_27

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DOI: 10.1007/978-94-009-0223-7_27

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