A mathematician once posed a deceptively simple question. Can a single 2-D conveyor belt be stretched around a set of wheels such that the belt is taut and touches every wheel without crossing itself?
MIT computer scientist Erik Demaine pondered the problem. For just a few wheels, the solution is easy: Arrange four into a square, wrap the belt around the outside, and the problem is solved — one version of it, at least.
“The question is whether it’s always possible to solve no matter how you draw the wheels,” Demaine says. A complete solution would lay out a set of rules that applies to every possible wheel arrangement and number. “But so far every algorithm we’ve come up with has been foiled.”
One day Demaine was working on the problem with his dad, who happens to be an artist and mathematician, and a colleague. The trio got stuck. So they decided to take a break with another activity the Demaines enjoy: designing new fonts. The team stuck thumbtacks into poster board to represent wheels, and wrapped them with rubber band “conveyor belts” to form letters.“It became a game,” Demaine says. “One of us would put in some thumbtacks, and the other would say, “Oh, I see, it’s a ‘K’!”
Demaine and his father, MIT artist-in residence Martin Demaine, published the complete alphabet of conveyor belt letters in the Proceedings of the 7th International Conference on Fun with Algorithms in July along with four other typeface ideas sparked by math and computational geometry. The Demaines’ interest in geometric folding spurred creation of three fonts, one of which — the “origami maze” typeface — uses a computer algorithm to create crease patterns that can fold into 3-D letters.
Several of the Demaines’ fonts can be turned into geometry or math puzzles. In the conveyor belt font, for example, take the belt away from a letter and all that’s left is a cryptic arrangement of wheels. “You can hide secret messages this way,” Erik Demaine says.
Another puzzle font, called the glass-squishing typeface, drew inspiration from their passion for glass blowing. After inventing a software program that helps glass blowers design pieces, the Demaines wanted to mathematically describe how pieces of glass squish together when heated. They started experimenting by making actual glass letters.
The duo arranged blue glass sticks around clear discs, popped the patterns into a volcano-hot oven and then pushed the softened pieces together. “We’d say, ‘Ah, I think this will make an ‘A,’ ” Demaine says, “Then we’d squish it and it would come out looking nothing like an ‘A’.”
After a week of experiments, they posted videos of the full alphabet on Demaine’s website (see erikdemaine.org/fonts). Now, they’re hoping to use what they have learned with the letters to build new software for their virtual glass program.
Demaine thinks the fonts are a fun way to introduce people to the world of computational geometry.
“We want people to play with the fonts,” he says. “We really love puzzles — now anyone can participate.”
A mishmash of what looks like sticks and bubbles morphs into letters that spell the words “Science News” in a font inspired by glass blowing. Once the glass sticks heat up, metal bars squish the pieces together around glass discs, forming letters. Credit: E. Demaine and M. Demaine