6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)
[Problem Session Notes]
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
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