The Theory The Theory and Practiceand Practiceof Origamiof Origami
Erik DemaineErik DemaineM.I.T.M.I.T.
OrigamiOrigami
Perhaps as old as paper itself (105 AD) Revolution in complex
origami design overpast ~25 years
Satoshi Kamiya Satoshi Kamiya
Joel Cooper
Brian Chan
Goran Konjevod
Origami USAOrigami USAConventionConvention
20092009
Folding Anything (in Theory) Folding Anything (in Theory) [Demaine, Demaine, Mitchell 1999][Demaine, Demaine, Mitchell 1999]
Theorem: Any 2D or 3D shapecan be folded from a square of paper
Tree Method of Origami Tree Method of Origami DesignDesign [Fujimoto, Kamiya, Kawahata, Lang, Maekawa, Meguro, [Fujimoto, Kamiya, Kawahata, Lang, Maekawa, Meguro, Yoshino]Yoshino]
[Lang, Demaine, Demaine 2006– [Lang, Demaine, Demaine 2006–2008]2008]
Tomohiro Tachi
Algorithm to fold any polyhedral surface
TomohiroTachi
Origamizer Origamizer [Tachi [Tachi 2006; Demaine & Tachi 2006; Demaine & Tachi 2009]2009]
““Self-Folding” OrigamiSelf-Folding” Origami
“hyperbolic paraboloid”
KennyKenny
Thermal origami[Cheung 2008]
Metal FoldingMetal FoldingMetal folding
Demaine, Demaine,Tachi, 2008
Fold polygons at cornersinstead of lines
Hinged DissectionHinged Dissection[first used by Kelland 1864][first used by Kelland 1864]
[Dudeney 1902]
Hinged Dissection UniversalityHinged Dissection Universality[Abbott, Abel, Charlton, Demaine, Demaine, Kominers [Abbott, Abel, Charlton, Demaine, Demaine, Kominers 2008] 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 TetrahedraRight-Angle Tetrahedra[Millibiology project: MIT, Harvard, [Millibiology project: MIT, Harvard, Makani]Makani]
Millibiology ProjectMillibiology Project[MIT CBA][MIT CBA]
ProteinProteinFoldingFolding
ribosome
The Theory The Theory and Practiceand Practiceof Origamiof Origami
Erik DemaineErik DemaineM.I.T.M.I.T.