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March 2017 The number of paperfolding curves in a covering of the plane
Francis Oger
Hiroshima Math. J. 47(1): 1-14 (March 2017). DOI: 10.32917/hmj/1492048844

Abstract

This paper completes our previous one in the same journal (vol. 42, pp. 37– 75). Let $\mathscr{C}$ be a covering of the plane by disjoint complete folding curves which satisfies the local isomorphism property. We show that $\mathscr{C}$ is locally isomorphic to an essentially unique covering generated by an $\infty$-folding curve. We prove that $\mathscr{C}$ necessarily consists of 1, 2, 3, 4 or 6 curves. We give examples for each case; the last one is realized if and only if $\mathscr{C}$ is generated by the alternating folding curve or one of its successive antiderivatives. We also extend the results of our previous paper to another class of paperfolding curves introduced by M. Dekking.

Citation

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Francis Oger. "The number of paperfolding curves in a covering of the plane." Hiroshima Math. J. 47 (1) 1 - 14, March 2017. https://doi.org/10.32917/hmj/1492048844

Information

Received: 18 August 2014; Revised: 13 June 2016; Published: March 2017
First available in Project Euclid: 13 April 2017

zbMATH: 1378.52021
MathSciNet: MR3634258
Digital Object Identifier: 10.32917/hmj/1492048844

Subjects:
Primary: 05B45
Secondary: 52C20, 52C23

Rights: Copyright © 2017 Hiroshima University, Mathematics Program

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Vol.47 • No. 1 • March 2017
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