1. The Theory and Practiceof Origami Erik Demaine M.I.T.

2. Origami • Perhaps as old as paper itself (105 AD) • Revolution in complexorigami design overpast ~25 years Satoshi Kamiya Satoshi Kamiya

3. Origami USAConvention2009 Brian Chan Joel Cooper Goran Konjevod

4. Folding Anything (in Theory) [Demaine, Demaine, Mitchell 1999] • Theorem: Any 2D or 3D shapecan be folded from a square of paper

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

6. Origamizer[Tachi 2006; Demaine & Tachi 2009] TomohiroTachi • Algorithm to fold any polyhedral surface Tomohiro Tachi

7. “Self-Folding” Origami “hyperbolic paraboloid”

8. Kenny Thermal origami[Cheung 2008]

9. Metal Folding Metal folding Demaine, Demaine,Tachi, 2008

10. Hinged Dissection[first used by Kelland 1864] • Fold polygons at cornersinstead of lines [Dudeney 1902]

11. Hinged Dissection Universality[Abbott, Abel, Charlton, Demaine, Demaine, Kominers 2008] • Theorem: For any finite setof polygons of equal area, there is a hinged dissection that can fold into any of the polygons,continuouslywithout self-intersection • Generalizes to 3D

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

13. Millibiology Project[MIT CBA]

14. ribosome ProteinFolding

15. The Theory and Practiceof Origami Erik Demaine M.I.T.