This Course at MIT

This Course at MIT pages provide context for how the course materials published on OCW were used at MIT. They are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

Course Overview

This page focuses on the course 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra as it was taught by Prof. Erik Demaine in Fall 2012.

This course is about folding forms, which encompasses any kind of reconfigurable structure that can change shape dynamically. There is a lot of excitement about applying folding to various disciplines such as science and engineering. The applications motivate the underlying mathematics of how to understand reconfigurable structures, the algorithms of how to fold your robotic arm into a desired shape, and even how to design new origami or new folding structures that do whatever you want.

Course Outcomes

Course Goals for Students

  • To appreciate the mathematics and algorithms behind analyzing and designing physical folds
  • To develop a thorough understanding of recently proven results to folding problems
  • To gain experience in working on open problems in the field
 

Curriculum Information

Prerequisites

6.046J/18.410J Design and Analysis of Algorithms, or equivalent background in discrete mathematics and algorithms. Alternatively, permission from the instructor.

Requirements Satisfied

H-Level graduate credit

Offered

Every other fall semester

The Classroom

  • Tiered lecture hall with chalkboards and projector at the front of the room and grouped seating for students.

    Class Session

    The professor used both the chalkboards and presentation slides, containing images and videos, for teaching during class sessions.

  • Classroom with sliding chalkboards and separate tablet armchairs.

    Open-Problem Session (Optional)

    Students worked together to brainstorm and hopefully solve open problems relevant to the content covered in the respective week’s class session.

 

Grading

The students' grades were based on the following activities:

 
The color used on the preceding chart which represents the percentage of the total grade contributed by reading questions and in-class questions. 10% Attendance
The color used on the preceding chart which represents the percentage of the total grade contributed by problem sets. 10% Class participation
The color used on the preceding chart which represents the percentage of the total grade contributed by the first exam. 20% Assignments
The color used on the preceding chart which represents the percentage of the total grade contributed by the second exam. 60% Final project
 
 

Student Information

On average, 30 students take this course each time it is offered.

Breakdown by Year

2/3 undergraduate upperclassmen; 1/3 graduate students

Breakdown by Major

Mainly Electrical Engineering and Computer Science majors and Mathematics majors, with a few Architecture majors

Typical Student Background

Prof. Demaine reflects on the range of students that enroll in this course:

“This is a graduate course, so while it’s ostensibly for graduate students, there are very advanced MIT undergraduates who choose to take the course—occasionally even a freshman! Usually more upperclassmen undergrads take this course because they have run out of undergraduate courses to take and want to take cool graduate courses.

While 6.849 gets a lot of students from computer science and mathematics, we usually also get between three to five architects, which is a fun challenge for me because they have a really strong design background and come up with interesting applications for folding that I don’t always think about. While that has led in a lot of cool directions, their mathematics background is a bit weaker so I have tried to make the course as broadly accessible as possible. I have crafted the content so that it still captures the mathematical spirit without always going into the details of the proofs, or at least minimally so that they can be appreciated by those with a more intuitive, geometric understanding as opposed to a rigorous mathematics background.”

 

How Student Time Was Spent

During an average week, students were expected to spend 12–14 hours on the course, roughly divided as follows:

Class Session

2 hours per week
  • Met 2 times per week for 1 hour per session; 24 sessions total
  • The professor led most class sessions by addressing submitted questions, covering additional content and applications, and facilitating in-class folding exercises.
  • The last four class sessions were set aside for students to present their final projects.
 

Out of Class

10 hours per week
  • Students were asked to watch a 1.5-hour video lecture prior to each respective class session.
  • For the first few weeks, problem sets were assigned. These short homework assignments then gave way to students’ individual research on their final projects.
 

Open-Problem Sessions (Optional)

2 hours per week
  • Students were encouraged to attend optional sessions during which they worked to solve open problems that are currently being worked on in the field. To read more about these sessions, see Open-Problem Sessions and Collaboration.
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. No classes throughout MIT. No session scheduled. Class session; optional problem solving session. No session scheduled.
2 Lecture session (on video). Class session. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
3 Lecture session (on video). Class session; problem set due. Lecture session (on video). Class session; optional problem solving session. No classes throughout MIT.
4 Lecture session (on video). Class session; problem set due. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
5 Lecture session (on video). Class session; problem set due. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
6 No classes throughout MIT. No classes throughout MIT. Lecture session (on video). Class session; problem set due; optional problem solving session. No session scheduled.
7 Lecture session (on video). Class session. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
8 Lecture session (on video). Class session; problem set due. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
9 No session scheduled. No session scheduled. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
10 Lecture session (on video). Class session. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
11 Lecture session (on video). Class session. Lecture session (on video). Class session; optional problem solving session. No session scheduled.
12 Lecture session (on video). Class session. No session scheduled. No classes throughout MIT. No classes throughout MIT.
13 No session scheduled. In-class student presentations. No session scheduled. In-class student presentations; optional problem solving session. No session scheduled.
14 No session scheduled. In-class student presentations. No session scheduled. No session scheduled. No session scheduled.
15 No session scheduled. In-class student presentations; project deliverable due. No session scheduled. No classes throughout MIT. No classes throughout MIT.
16 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
Displays the color and pattern used on the preceding table to indicate dates when classes are not held at MIT. No classes throughout MIT
Displays the color used on the preceding table to indicate dates when class sessions are held. Class session
Displays the color used on the preceding table to indicate dates when in-class student presentations are held. In-class student presentations
Displays the symbol used on the preceding table to indicate dates when problem sets are due. Problem set due date
Displays the color used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the color used on the preceding table to indicate dates when lecture sessions are held. Lecture session (on video)
Displays the color used on the preceding table to indicate dates when optional open-problem sessions are held. Open-problem session (optional)
Displays the symbol used on the preceding table to indicate dates when project deliverables are due. Project deliverable due date
 

Instructor Insights

The idea is to get students engaged and interested in pushing the frontiers of research and trying to solve the problems to which no one yet knows the answers.

—Prof. Erik Demaine

In the following pages, Prof. Demaine describes various aspects of how he teaches 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra.