Past Winner
2003 NSERC Doctoral Prize

Erik Demaine

Information Technology

University of Waterloo

Dr. Erik Demaine's life is unfolding in wondrous ways. Which is apt for a mathematical prodigy in computational origami — the geometry of paper folding.

The winner of a 2003 Natural Sciences and Engineering Research Council (NSERC) Doctoral Prize — one of Canada's premier graduate student awards — Dr. Demaine was home schooled by his father from age seven, toppled Dalhousie University's age barrier by being admitted at 12, and now at 21 is the youngest professor at the Massachusetts Institute of Technology.

The University of Waterloo graduate's doctoral thesis solved what's known as the Carpenter's Rule Problem.

"It's a sexy problem," says Dr. Demaine from his office at MIT. "It's a very attractive problem because it's very simple to state. And yet it was very hard to solve. The problem goes back about 25 years and dozens of people had worked on it, though no one could solve it."

The problem gets its name from the real carpenter's ruler: a series of rods or bars connected together by joints so that it can fold into a compact form. In the Carpenter's Rule Problem, the joints are assumed to be able to fold to any angle.

The question is: Is it always possible to fold the chain while it's flat on the table from one configuration into any other configuration without any of the bars crossing one another?

It's more than a kind of "Rubik's Cube" puzzle for geniuses. Understanding the possibilities and limits of folding and unfolding in general is important to a wide range of applications, from sheet metal fabrication to airbag storage and bioinformatics, where the math is used to understand, and perhaps predict, how proteins fold. The Carpenter's Rule Problem also applies directly to the design of robotic arms used in industry.

"The answer is yes," says Dr. Demaine. Though he cautions that the Carpenter's Rule solution doesn't apply to 3-D movement, so the makers of robotic arms like the Canadarm need to pay careful attention to how the arm is constructed.

"You needed the right people, with the right points of view to solve the problem," explains Dr. Demaine of his several year off-and-on journey to crack this geometric riddle. The solution was achieved through collaboration with Dr. Robert Connelly, an expert in rigidity theory at Cornell University, and Dr. Günter Rote, an expert in geometric optimization at the Free University Berlin.

"Collaboration is a big part of what I do," says Dr. Demaine, who has co-authored more than 100 scientific papers with, at latest count, 96 colleagues.

Prior to the Carpenter's Rule Problem, Dr. Demaine had already cut his teeth on numerous complex folding questions. During doctoral research with his supervisors, Drs. Anna Lubiw and Ian Munro, he created the proof for what's known as the Fold and Cut Problem. In a paper co-authored with his father (now a visiting scientist at MIT) and others, they showed that it's possible to create any straight-sided shape, from a simple star to a breathtaking dragon, by folding a piece of paper in a specific way and then making a single cut through it.

At present, he's still at work on folding questions, including probing the limits of building 3-D objects from a single piece of cut sheet metal.