O. Aichholzer, G. Aloupis, E. D. Demaine, M. L. Demaine, S. P. Fekete,
M. Hoffmann, A. Lubiw, J. Snoeyink, and A. Winslow
Can folding a piece of paper flat make it larger? We explore whether a shape
must be scaled to cover a flat-folded copy of itself. We consider both
single folds and arbitrary folds (continuous piecewise isometries
). 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.