origami: a blend of sculpture + mathematics

Artist and MIT professor Erik Demaine makes flat geometric diagrams spring into elegant, three-dimensional origami sculptures.

By Marina Koren, SMITHSONIAN.COM, JANUARY 23, 2013

green-cycles-origami-600
This origami structure, called “Green Cycles,” by Erik Demaine and his father Martin required a week of improvisation to assemble. Credit: Renwick Gallery

The shape of a Pringle, mathematically speaking, is called a hyperbolic paraboloid. Artists have been folding paper into this shape for years. The twist? Hyperbolic paraboloids shouldn’t exist in origami—it’s impossible to make such a 3D shape using only the creases pressed into paper by hand.

By that logic, some of Erik Demaine’s artwork shouldn’t exist either.

Demaine, the world’s top computational origami theorist, has created a series of sculptures by folding concentric squares into square pieces of paper, alternating mountain and valley, and folding the diagonals. With each sculpture, the paper pops into a saddle shape called a hyperbolic paraboloid and stays there. Its accordion-like folds are pretty to look at, but Demaine, a computer science professor at MIT, isn’t sure how it works.

Once the paper is folded, the entire structure settles into a natural form. “Physics finds that balance,” Demaine says. But, the mechanisms of the Pringle-like shape are still poorly understood. Demaine posits there must be little creases in the paper invisible to the naked eye, as handmade folds alone can’t account for the end shape.

Trying to solve this mystery means marrying sculpture and mathematics.

“We’ve come up with a math problem that inspires new art—and an art problem that inspires new math,” says Demaine. The 31-year-old artist creates his origami sculptures with his father Martin.

The final product, “Green Cycles” (pictured at top), was created using two different colored sheets of French-made Mi-Teintes watercolor paper, bonded together. Using a ball burnisher, which is essentially a ballpoint pen without the ink, the Demaines pushed the two-layer sheet into rings of concentric circles carved into a wood template. The paper is scored along the circular creases and cut into a donut shape, before it springs into a three-dimensional form. The artist creates several of these models and loops them together into an interlocking paper sculpture. The younger Demaine says the hardest part is assembly, which takes up to a week, because they can’t predict if the resulting shapes will twist around one another to create a solid, aesthetically pleasing piece.

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