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