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 Folding Metal foldingDemaine, 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.