This class reviews Carpenter's Rule and properties of pseudotriangulation. Various proofs are presented, which cover topics including non-zero stresses, linear and equilateral locked trees, and unfolding of 4D chains.

1. Lecture 1: Overview
2. Class 1: Overview
3. Lecture 2: Simple Folds
4. Class 2: Universality & Simple Folds
5. Lecture 3: Single-Vertex Crease Patterns
6. Class 3: Single-Vertex Crease Patterns
7. Lecture 4: Efficient Origami Design
8. Class 4: Efficient Origami Design
9. Lecture 5: Artistic Origami Design
10. Class 5: Tessellations & Modulars
11. Lecture 6: Architectural Origami
12. Class 6: Architectural Origami
13. Lecture 7: Origami is Hard
14. Class 7: Origami is Hard
15. Lecture 8: Fold & One Cut
16. Class 8: Fold & One Cut
17. Lecture 9: Pleat Folding
18. Class 9: Pleat Folding
19. Lecture 10: Kempe's Universality Theorem
20. Class 10: Kempe's Universality Theorem
21. Lecture 11: Rigidity Theory
22. Class 11: Generic Rigidity
23. Lecture 12: Tensegrities & Carpenter's Rules
24. Class 12: Tensegrities
25. Lecture 13: Locked Linkages
26. Class 13: Locked Linkages
27. Lecture 14: Hinged Dissections
28. Class 14: Hinged Dissections
29. Lecture 15: General & Edge Unfolding
30. Class 15: General & Edge Unfolding
31. Lecture 16: Vertex & Orthogonal Unfolding
32. Class 16: Vertex & Orthogonal Unfolding
33. Lecture 17: Alexandrov's Theorem
34. Class 17: D-Forms
35. Lecture 18: Gluing Algorithms
36. Lecture 19: Refolding & Smooth Folding
37. Class 19: Refolding & Kinetic Sculpture
38. Lecture 20: Protein Chains
39. Class 20: 3D Linkage Folding
40. Lecture 21: HP Model & Interlocked Chains

This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course.

This is an advanced class on computational geometry focusing on folding and unfolding of geometric structures including linkages, proteins, paper, and polyhedra. Examples of problems considered in this field include:

- What forms of origami can be designed automatically by algorithms?
- What shapes can result by folding a piece of paper flat and making one complete straight cut?
- What polyhedra can be cut along their surface and unfolded into a flat piece of paper without overlap?
- When can a linkage of rigid bars be untangled or folded into a desired configuration?

Many folding problems have applications in areas including manufacturing, robotics, graphics, and protein folding. This class covers many of the results that have been proved in the past few years, as well as the several exciting open problems that remain open.