The computer scientist and his father have been pushing the limits of paper folding for years. A decade ago they were featured in a PBS documentary about the art form, and their sculptures are part of the permanent collection at the Museum of Modern Art.
The pair started working together when they were 6 years old.
The son of a mathematician and a visual artist, he eventually taught Martin advanced math and computer science.
Their newest work, a mathematical proof, takes the collaboration to a new extreme: a realm where shapes collapse after being scored with many creases. They had a hard time accepting the idea at first.
We debated for a while if this was legit. Is this a real thing, said the new work's author,Erik Demaine, along with his co-authors from MIT, Jin-ichi Itoh of Sugiyama Jogakuen University, and the National University of Singapore.
The new work was published in the journal Computational Geometry in October after being posted online last May. They wanted to know if it was possible to take any polyhedral shape and fold it flat.
It isn't allowed to cut or tear the shape. The shape's intrinsic distances must be preserved. The paper must not pass through itself because that doesn't happen in the real world. It is especially challenging when everything is moving in 3D. The constraints mean that squashing the shape won't work.
The proof shows that you can accomplish this folding if you use an infinite-creasing strategy, but it begins with a more down-to-earth technique that four of the same authors introduced in a 2015 paper.
They studied the folding question for a simpler class of shapes: orthogonal polyhedra whose faces meet at right angles and are aligned with at least one of the x, y and Z coordinate axes. Meeting these conditions forces the faces of a shape to be rectangular, which makes folding simpler than collapsing a refrigerator box.
It's easy to figure out because each corner looks the same. It is just two planes meeting in a straight line.
The father and son team have collaborated on many projects. Over a decade ago, they worked with Sarah Eisenstat and Andrew Winslow to find the mathematical relationship between the number of squares on a Rubik's cube and the number of moves it takes to solve that cube.
Photograph: Dominick Reuter/MIT
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