Organizational Note: This course was taught with an inverted lecture format. Students first watched lecture videos from the last time the course was offered, in Fall 2010. Class time was devoted to in-depth discussions of the topics covered in those lectures, and additional activities such as demonstrations, proofs, and folding exercises. The materials here are presented in accordance with the way the course was organized in Fall 2012, which differed from the previous offering. As a result, some of the videos, notes, and slides from Fall 2010 are not in sequential order, but rather one that is most relevant to the inverted format.
|SES #||TOPICS & DESCRIPTIONS||LECTURE RESOURCES (FROM FALL 2010)||CLASS RESOURCES|
|1||Overview of the course: Inverted lecture format, sample topics and problems considered.|| |
Video of Lecture 1 (optional)
Video of Class 1
Origami intro: Origami alphabet, higher dimensions.
Universality: Terminology history, practical strip folding, pseudopolynomial bounds, seam placement, hide gadget via simple folds?
Simple folds: Metal/wood/plastic motivation, definition, examples, linear-time algorithm, extra creases.
Video of Lecture 2
Video of Class 2
Single-vertex crease patterns: Linear-time algorithm, local foldability examples, T-shirt folding, higher dimensions, why flat foldability?
Video of Lecture 3
Video of Class 3
Efficient origami design: Uniaxial, TreeMaker and Origamizer in practice, box-pleating tree method, tree method triangulation, universal molecule, gift wrapping, checkerboard gadgets, Origamizer software vs. mathematics, vertex/edge tucking molecules, Voronoi diagrams.
Video of Lecture 4
Video of Class 4
Artistic origami design: Jason Ku designs, other materials (dollars, cardboard, hydro, metal, polypropylene), tessellations, Tess, connected cranes, modular origami, business card cubes.
Video of Lecture 5
Slides and video courtesy of Jason Ku. Used with permission.
Video of Class 5
Architectural Origami: Origamizer, Freeform Origami, Rigid Origami Simulator.
Video of Lecture 6
Slides and video courtesy of Tomohiro Tachi. Used with permission.
Video of Class 6
Universal hinge patterns: Box-pleating history, maze-folding prints.NP-hardness: Simple foldability, crease pattern flat foldability.
Video of Lecture 7
Video of Class 7
Fold and one cut: Software, scissor vs. mathematical cuts, tree folding, density, examples, how many disks, comparison to tree method, continuous flattening.
Video of Lecture 8
Video of Class 8
Pleat folding: Triangulated hypars, smoothness, normals, mathematical vs. real paper, pleat folding algorithms, hypar folding.
Video of Lecture 9
Video of Class 9
Folding motions: Trouble with holes.
Linkages to sign your name: Sliding joints, contraparallelogram bracing, higher dimensions, semi-algebraic sets, splines.
Geometric construction: Straight edge and compass, origami axioms, angle trisection, cube doubling.
Video of Lecture 10
Video of Class 10
Rigidity theory: Pebble algorithms, rigid component decomposition, body-and-bar framework, angular rigidity, 5-connected double bananas.
Video of Lecture 11
|Notes for Class 11 (PDF - 3.2MB) |
Video of Class 11
Tensegrities: Dot products, springs, software, sculpture.
Video of Lecture 12
Video of Class 12
Locked linkages: Why expansiveness, energy algorithm correctness, pointed pseudotriangulations (combinatorics, rigidity, universality, expansiveness, extremeness), linear equilateral trees can't lock, unfolding 4D chains.
Video of Lecture 13
Video of Class 13
Hinged dissections: Animations, polyform inductive construction, rectangle to rectangle, furniture, pseudopolynomial construction, 3D, Dehn invariant.
Video of Lecture 14
Video of Class 14
Polyhedron unfolding: Handles, holes, ridge trees; sun unfolding; zipper unfolding; more ununfoldable polyhedra; NP-completeness of edge unfolding; band unfolding; continuous blooming.
Video of Lecture 15
Video of Class 15
Polyhedron unfolding: Topologically convex vertex-ununfoldable polyhedron, unfolding orthogonal polyhedra with quadratic refinement.
Video of Lecture 16
Video of Class 16
Polyhedron folding: Pita forms, D-forms, seam forms, convex hull and crease properties, rolling belts, Burago-Zalgaller folding into nonconvex polyhedra.
Video of Lecture 17
Video of Class 17
Watch origami documentary Between The Folds.
Video of Lecture 18
|No class resources for this session|
Polyhedron refolding: Fractal unfolding, three boxes, flat boxes.
Kinetic sculpture: Theo Jansen's Strandbeests, Arthur Ganson.
Video of Lecture 19
Video of Class 19
3D linkage folding: ribosomes, HP protein folding NP-hardness, flattening is strongly NP-hard, flips, flipturns, deflations, pops, popturns.
Video of Lecture 20
Video of Lecture 21
Video of Class 20
|21–24||Student presentations||No lecture resources for these sessions||No class resources for these sessions|