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

Prof. Erik Demaine TA: Jayson Lynch

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Overview

the algorithms behind building TRANSFORMERS and designing ORIGAMI

Whenever you have a physical object to be reconfigured, geometric folding often comes into play. This class is about algorithms for analyzing and designing such folds. Motivating applications include

automated design of new and complex origami
transforming robots by self-folding sheets or chains
how to fold robotic arms without collision
how to bend sheet metal into desired 3D shapes
understanding how proteins fold

Major progress have been made in recent years in many of these directions, thanks to a growing understanding of the mathematics and algorithms underlying folding. Nonetheless, many fundamental questions remain tantalizingly unsolved. This class covers the state-of-the-art in folding research, including a variety of open problems, enabling the student to do research and advance the field.

This year we will be experimenting with online lectures. Students will be expected to watch recorded lectures, allowing in-class time to be more interactive through folding experiments, answering questions, collaborative projects, clarifying proofs, and exploring new results and applications.

We will organize an optional problem-solving session, during which we can jointly try to solve open problems in folding. In the past, these sessions have led to important new results and published papers, as well as class projects.

Class projects more generally can take the form of folding-inspired sculptures; formulations of clean, new open problems; implementations of existing algorithms; or well-written descriptions of one or more papers in the area. Projects can be purely mathematical (geometric) and/or theoretical computer science (algorithmic/complexity theoretic) and/or artistic. Students are also required to do a project presentation and a small number of problem sets.

Topics

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:

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.

Textbook

The textbook for the class is Geometric Folding Algorithms: Linkages, Origami, Polyhedra by Erik Demaine and Joseph O'Rourke, published by Cambridge University Press (2007). The list price for the hardback is $107. Some copies will be available at the MIT Coop at this price. Amazon offers a sale price of $88. A further reduced price is available as part of a bulk class purchase; let Erik know if you want to be part of it.

Additional recommended reading is Origami Design Secrets: Mathematical Methods for an Ancient Art by Robert Lang.

Specifics

Lecture Time:	Tuesdays and Thursdays at 10:00am–11:00am
Lecture Room:	MIT room 3-370
First Lecture:	Thursday, September 6, 2012
Problem Session Time:	Thursdays at 5pm-7pm
Problem Session Room:	56-180
Professor:	Erik Demaine, 32-G680
TA:	Jayson Lynch, 32-G635
Staff Email:	6849-staff at csail.mit.edu
Units:	3-0-9
Prerequisites:	6.046 or equivalent background in discrete mathematics and algorithms Alternatively, permission from the instructor.
Credit:	H-level and EC-level credit; no ED credit
Requirements:	Written project and project presentation. Small number of problem sets.

Participating

We welcome both undergraduate and graduate students from all universities, although officially this is a graduate class.

If you are interested in attending the class, for credit or as a listener, please join the 6849-students mailing list.

Previous Offerings

This class was offered in Fall 2010, Fall 2007 (as 6.885), and Fall 2004 (as 6.885). You might be interested in the lecture notes, problem sets, etc. from those offerings.

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