6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)

Prof. Erik Demaine       TA: Jayson Lynch


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[+] 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.

This class is structured around the many excellent questions that students asked and suggestions they made. There are so many that I've marked a few highlights with stars:
  • ★ Actual folding (we'll fold the numerals 6, 8, 4, 9 from an origami alphabet!)
  • Some history of where a few terms come from.
  • Practical examples of strip folding.
  • Pseudopolynomial bounds on strip folding: what they are and what's (un)known.
  • Seam placement (some skipped content in L02's notes)
  • ★ Open problem about simply folding the hide gadget: let's solve it together!
  • Motivation for simple folds: metal/wood/plastic bending
  • Definition of simple folds: more precise
  • Examples of flat-foldable vs. mingling 1D mountain-valley patterns
  • ★ Algorithm for testing 1D flat foldability in linear time (new -- simpler than textbook!)
  • Making any mountain-valley pattern flat foldable by adding extra creases
  • Higher-dimensional folding

Download Video: 360p, 720p

Handwritten notes, page 1/5[previous page][next page][PDF]

Handwritten notes, page 1/5[previous page][next page][PDF]

Slides, page 1/32[previous page][next page][PDF]

Slides, page 1/32[previous page][next page][PDF]

The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The handwritten notes and slides should advance automatically. If you have any trouble with playback, email Erik.