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Covering Folded Shapes

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Publication:2968115

DOI10.20382/JOCG.V5I1A8zbMATH Open1408.51019arXiv1405.2378OpenAlexW2137142766MaRDI QIDQ2968115

Author name not available (Why is that?)

Publication date: 9 March 2017

Abstract: Can folding a piece of paper flat make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries SightarrowR2). The underlying problem is motivated by computational origami, and is related to other covering and fixturing problems, such as Lebesgue's universal cover problem and force closure grasps. In addition to considering special shapes (squares, equilateral triangles, polygons and disks), we give upper and lower bounds on scale factors for single folds of convex objects and arbitrary folds of simply connected objects.


Full work available at URL: https://arxiv.org/abs/1405.2378




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