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POINTS IN A FOLD

Part of: Elementary number theory

Published online by Cambridge University Press:  10 January 2022

MARTIN BUNDER ,
KEITH TOGNETTI  and
BRUCE BATES
MARTIN BUNDER*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia
KEITH TOGNETTI
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia e-mail: tognetti@uow.edu.au
BRUCE BATES
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia e-mail: bbates@ouw.edu.au
*
e-mail: mbunder@uow.edu.au
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Abstract

When a page, represented by the interval $[0,1],$ is folded right over left $ n$ times, the right-hand fold contains a sequence of points. We specify these points and the order in which they appear in each fold. We also determine exactly where in the folded structure any point in $[0,1]$ appears and, given any point on the bottom line of the structure, which point lies at each level above it.

Keywords

paperfoldingprefoldsfolds

MSC classification

Primary: 11A55: Continued fractions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 1 , August 2022 , pp. 7 - 17
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

Bates, B. P., Bunder, M. W. and Tognetti, K. P., ‘Mirroring and interleaving in the paperfolding sequence’, Appl. Anal. Discrete Math. 4 (2010), 96–118.Google Scholar
Dekking, F. M., Mendès France, M. and van der Poorten, A. J., ‘Folds!’, Math. Intelligencer 4 (1982), I: 130–138; II: 173–181; III: 190–195.Google Scholar
Mendès France, M., Shallit, J. and van der Poorten, A. J., ‘On lacunary formal power series and their continued fraction expansion’, in: Number Theory in Progress: Proceedings of the International Conference in Honour of A. Schinzel, Zakopane 1997, Vol. 1 (eds. Györy, K., Iwaniec, H. and Urbanowicz, J.) (de Gruyter, Berlin, 1999), 321–326.Google Scholar
Mendès France, M. and van der Poorten, A. J., ‘Arithmetic and analytical properties of paper folding sequences’, Bull. Aust. Math. Soc. 24 (1981), 123–131.CrossRefGoogle Scholar
Shallit, J., The Online Encyclopedia of Integer Sequences, A281589 #17, https://oeis.org/A281589.Google Scholar
Sigrist, R., The Online Encyclopedia of Integer Sequences, A281589 #5, https://oeis.org/A281589.Google Scholar
van der Poorten, A. J. and Shallit, J. O., ‘Folded continued fractions’, J. Number Theory 40 (1992), 237–250.CrossRefGoogle Scholar