the theory and practice of origami erik demaine m.i.t

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  • The Theory and Practiceof OrigamiErik DemaineM.I.T.

  • OrigamiPerhaps as old as paper itself (105 AD)Revolution in complex origami design over past ~25 yearsSatoshi KamiyaSatoshi Kamiya

  • Joel CooperBrian ChanGoran KonjevodOrigami 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 20062008]

  • Tomohiro TachiAlgorithm to fold any polyhedral surfaceTomohiro TachiOrigamizer [Tachi 2006; Demaine & Tachi 2009]

  • Self-Folding Origamihyperbolic paraboloid

  • KennyThermal origami [Cheung 2008]

  • Metal FoldingMetal foldingDemaine, Demaine, Tachi, 2008

  • Fold polygons at corners instead of linesHinged 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-intersectionGeneralizes to 3D

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

  • Millibiology Project[MIT CBA]

  • ProteinFolding

  • The Theory and Practiceof OrigamiErik DemaineM.I.T.

    *right photo is http://farm3.static.flickr.com/2124/2070841756_ae109a7093_b.jpg from http://www.flickr.com/photos/hyougushi/2070841756/sizes/l/ from http://www.flickr.com/photos/hyougushi/2070841756/*http://farm3.static.flickr.com/2611/3675305492_be557219d7_b.jpg from http://www.flickr.com/photos/vipnyc/3675305492/sizes/l/in/photostream/ from http://www.flickr.com/photos/vipnyc/3675305492/in/photostreamRest are crops from http://erikdemaine.org/photos/OrigamiUSA_June2009/**http://www.webdesignofmaine.com/images/samples/big_horse.jpgalternative: http://www.web3dservice.com/3D/real_time/horse_3dmodel.jpg*http://farm2.static.flickr.com/1227/1003649096_2389cfa0ca_b.jpg from http://www.flickr.com/photos/tactom/1003649096/sizes/l/ from http://www.flickr.com/photos/tactom/1003649096/urethane membrane; urethane + expanding acrylic microspheres composite creases2-part mold with rivers for creases, syringe to fill creases**What is a hinged dissection

    The big open problem

    Weve solved it (but dont reveal answer)Working on pseudopolynomial, which is best you can hope for (even without hinging)**

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