COVERING FOLDED SHAPES *

Oswin Aichholzer, Greg Aloupis, Erik Demaine, Martin Demaine, Sándor Fekete, Michael Hoffmann, Anna Lubiw, Jack Snoeyink, Andrew Winslow
2014 JoCG   unpublished
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 S → R 2). 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
more » ... iangles, 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.
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