The Theory and Practice of Origami Erik Demaine M.I.T.

Origami  Perhaps as old as paper itself (105 AD)  Revolution in complex origami design over past ~25 years Satoshi Kamiya

Joel Cooper Brian Chan Goran Konjevod Origami USA Convention 2009

Folding Anything (in Theory) [Demaine, Demaine, Mitchell 1999]  Theorem: Any 2D or 3D shape can be folded from a square of paper

Tree Method of Origami Design [Fujimoto, Kamiya, Kawahata, Lang, Maekawa, Meguro, Yoshino] [Lang, Demaine, Demaine 2006–2008]

Tomohiro Tachi  Algorithm to fold any polyhedral surface Tomohiro Tachi Origamizer [Tachi 2006; Demaine & Tachi 2009]

“Self-Folding” Origami “hyperbolic paraboloid”

Kenny Thermal origami [Cheung 2008]

Metal Folding Metal folding Demaine, Demaine, Tachi, 2008

 Fold polygons at corners instead of lines Hinged Dissection [first used by Kelland 1864] [Dudeney 1902]

Hinged Dissection Universality [Abbott, Abel, Charlton, Demaine, Demaine, Kominers 2008]  Theorem: For any finite set of polygons of equal area, there is a hinged dissection that can fold into any of the polygons, continuously without self-intersection ▪Generalizes to 3D

Right-Angle Tetrahedra [Millibiology project: MIT, Harvard, Makani]

Millibiology Project [MIT CBA]

Protein Folding ribosome

The Theory and Practice of Origami Erik Demaine M.I.T.