Folding and Unfolding in Computational Geometry

Erik Demaine


Oct 1,



I will present several recent results about geometric folding and unfolding
problems.  For example, place several rigid rods down on the table, and hinge
them together at their ends to form a chain.  Is it always possible to fold the
hinges in such a way that the linkage is straightened into a line?  The rods
cannot change in length or cross each other, and must remain on the table.
While at first glance it may seem intuitive that any chain can be ``unraveled''
into a straight line, this ``carpenter's rule problem'' has proved difficult
and remained unsolved for over 25 years.

This problem was solved in a recent burst of interest in folding and unfolding, a branch of discrete and computational geometry. In the past few years, several intriguing and surprising results have been proved about various contexts of folding and unfolding: reconfiguring linkages, paper folding (origami), unfolding polyhedra into nonoverlapping ``nets,'' and gluing polygons into polyhedra. Many of these problems have applications in areas including manufacturing, robotics, and protein folding.

Return to Applied Math Colloquium home page