# InfoCoBuild

## 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra

6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012, MIT OCW). Instructor: Professor Erik Demaine. 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. (from ocw.mit.edu)

 Lecture 09 - Pleat Folding

This lecture introduces the hyperbolic paraboloid, hyparhedra, and the circular pleat. Topics include triangulated folding of the hypar, how paper folds between creases, and Gaussian curvature. Various proofs involving straight creases are given.

 Class 09 - Pleat Folding

This class covers creases in context of smoothness and a proof from the lecture involving Taylor expansion. Algorithms for the numbers of folding operations necessary for an MV string are presented. The class ends with a hypar folding exercise.

Go to the Course Home or watch other lectures:

 Lecture 01 - Overview Lecture 02 - Simple Folds Lecture 03 - Single-Vertex Crease Patterns Lecture 04 - Efficient Origami Design Lecture 05 - Artistic Origami Design Lecture 06 - Architectural Origami Lecture 07 - Origami is Hard Lecture 08 - Fold & One Cut Lecture 09 - Pleat Folding Lecture 10 - Kempe's Universality Theorem Lecture 11 - Rigidity Theory Lecture 12 - Tensegrities & Carpenter's Rules Lecture 13 - Locked Linkages Lecture 14 - Hinged Dissections Lecture 15 - General & Edge Unfolding Lecture 16 - Vertex & Orthogonal Unfolding Lecture 17 - Alexandrov's Theorem Lecture 18 - Gluing Algorithms Lecture 19 - Refolding & Smooth Folding Lecture 20 - Protein Chains Lecture 21 - HP Model & Interlocked Chains