The Theory
and Practice
of Origami
Erik Demaine
M.I.T.
Origami
 Perhaps as old as paper itself (105 AD)
 Revolution in complex
origami design over
past ~25 years
Satoshi Kamiya
Satoshi Kamiya
Origami USA
Convention
2009
Brian Chan
Joel Cooper
Goran Konjevod
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 2006–2008]
Origamizer [Tachi 2006;
Demaine & Tachi 2009]
 Algorithm to fold any
polyhedral surface
Tomohiro Tachi
Tomohiro
Tachi
“Self-Folding” Origami
“hyperbolic
paraboloid”
Kenny
Thermal origami
[Cheung 2008]
Metal Folding
Metal folding
Demaine, Demaine,
Tachi, 2008
Hinged Dissection
[first used by Kelland 1864]
 Fold polygons at corners
instead of lines
[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-intersection
▪ Generalizes to 3D
Right-Angle Tetrahedra
[Millibiology project: MIT, Harvard, Makani]
Millibiology Project
[MIT CBA]
Protein
Folding
ribosome
The Theory
and Practice
of Origami
Erik Demaine
M.I.T.