  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 $S\rightarrow
R^2$). 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 and disks), we give upper and
lower bounds on scale factors for single folds of convex objects and arbitrary
folds of simply connected objects.
