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Arithmetic and analytic properties of paper folding sequences

Published online by Cambridge University Press:  17 April 2009

M. Mendès France  and
A.J. van der Poorten
M. Mendès France
Affiliation:
UER de Mathématiques et d'Informatique, Université de Bordeaux I, 351 Cours de la Libération, 33405 Talence – Cédex, France;
A.J. van der Poorten
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, New South Wales 2113, Australia.
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Abstract

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The mechanical procedure of paper folding generates an uncountable family of infinite sequences of fold patterns. We obtain the associated Fourier series and show that the sequences are almost periodic and hence deterministic. Further, we show that paper folding numbers defined by the sequences are all transcendental.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1981 , pp. 123 - 131
Copyright
Copyright © Australian Mathematical Society 1981

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