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The minimal number of pieces realizing affine congruence by dissection of topological discs

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Abstract

Let \({\mathcal{G}}\) be a group of affine transformations of the plane that contains a strict contraction and all translations. It is shown that any two topological discs \(D,E \subseteq {\mathbb{R}}^2\) are congruent dissection with respect to \({\mathcal{G}}\) such that only three topological discs are used as pieces of dissection. Two pieces of dissection do not suffice in general even if \(\mathcal{G}\) consists of all affine transformations.

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  1. Equipe d'Analyse Université Paris VI Case 186, 4, Place Jussieu, 75252, Paris Cedex 05, France E-mail

    Christian Richter

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  1. Christian Richter
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Richter, C. The minimal number of pieces realizing affine congruence by dissection of topological discs. Periodica Mathematica Hungarica 46, 203–213 (2003). https://doi.org/10.1023/A:1025944327967

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  • DOI: https://doi.org/10.1023/A:1025944327967

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