6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Spring 2017)

Prof. Erik Demaine; Martin Demaine; Dr. Jason Ku; TAs Adam Hesterberg & 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
using 2D fabrication technology to manufacture complex 3D objects
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, and ask any questions they have via an online form. In-class time will be divided between answers to questions, new material presented by the professor and/or guest lecturers, and in-class problem solving (tackling solved and/or unsolved problems, as you like). To facilitate collaboration, we'll be using a new open-source software platform called Coauthor.

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). A further reduced price will likely be 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:	Wednesdays at 2:30pm–5:00pm
Lecture Room:	MIT room 54-100
First Lecture:	Wednesday, February 8, 2017
Office Hours:	Sundays 5-6pm in 32-G5 lounge Mondays 3-4pm in 32-G632
Professor:	Erik Demaine, 32-G680
Co-lecturers:	Martin Demaine, 32-G582 Jason Ku, 32-G616
TAs:	Adam Hesterberg, 32-G635 Jayson Lynch, 32-G580
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:	Participation in class, measured as posting or being @mentioned in at least one Coauthor post each week. Project write-up and presentation. Problem sets roughly weekly.

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 do the following:

Join the 6849-students mailing list.
Sign up for an account on Coauthor
Fill out this signup form

Previous Offerings

This class was offered in Fall 2012, 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.