Erik D. Demaine and Joseph S. B. Mitchell, “Reaching Folded States of a Rectangular Piece of Paper”, in Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG 2001), Waterloo, Ontario, Canada, August 13–15, 2001, pages 73–75.
Abstract:
We prove that any folded state of a rectangular piece of paper
(a continuous isometric non-self-intersecting mapping of the paper into space)
can be reached by a continuous folding process, starting from the unfolded
state, while at all times being a valid folding.
In our model, the paper cannot properly cross itself, but can touch itself,
as in a flat folding.
