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Art by the numbers

An exhibition in New York shows how geometry, algorithms and math formulas can create exciting works of art through the science of origami

Math Unfolded: An Exhibit of Mathematical Origami Art is like a cerebral vertex where art intersects with math. Left: Robert Lang's Cyclomatus Metallifer, Opus 562, (2010), is a large insect crawling over rocks. Right: Linen Swirls (2015) by son and father team Erik Demaine and Martin Demaine.

MENTION the word "math" and visions of high school arithmetic, thorny trigonometry and those prickly calculus derivatives often come to mind. But the world of math goes far beyond chalk-etched numbers and quadratic equations on a blackboard. It's also an art. Yes, an art.

And the National Museum of Mathematics is counting on its latest exhibit, Math Unfolded: An Exhibit of Mathematical Origami Art, to show math buffs and art fans alike how geometry, algorithms and math formulas can create exciting works of art through the science of origami.

"We believe that math and art are actually two sides of the same coin," said Cindy Lawrence, executive director and chief executive of the museum, known as MoMath. "Origami is a bridge between math and art that really does drive home the point that there is beauty in math and that math can be used to create beautiful objects."

Science of paper folding

Origami, put simply, is the science of paper folding. It combines geometry, patterns and math theory to transform a single piece of paper into a mind-boggling work of art - often a 3D sculpture.

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The origami exhibit, in a backroom on the museum's first floor, features 66 pieces of art made by 24 artists from around the world. Walking through the exhibit feels like strolling through an art gallery - far different from the hustle and bustle atmosphere of the main museum, where visitors boisterously play with interactive exhibits, like riding a square-wheeled tricycle on a circular surface, using math formulas to make the perfect shot through a basketball hoop, or remotely driving a car through a Möbius strip.

But the origami exhibit is different - almost a cerebral vertex where art intersects with math.

The exhibit features wildlife sculptures including a horse, jellyfish, squirrel, lobster and dragonfly, as well as masks, flowers and stars. The artists used carefully calculated folds, pleats and colour to create the art pieces. Some are showcased behind clear plastic cases; others hang from the ceiling and on the walls. And each comes with descriptions about the artist, the materials used, its connection to math, and how the art was created, in many cases, from a single piece of paper.

"They are very realistic pieces but they were designed with mathematical algorithms - most of them are folded from square pieces of paper with no cutting and no glue," said Wendy Zeichner, president and chief executive of Origami USA, who was co-curator of the exhibit with Charlene Morrow, the chairwoman of Origami USA's board.

Robert Lang, a rock star in the origami world who has six pieces in the MoMath exhibit, has been practising the art for more than 50 years. At the age of 6, he received a craft book that included a few pages on origami, with instructions on how to make a talking crow, flapping bird and other basic animals with folded paper. He was hooked.

His interest steadily grew through high school and college, where he studied engineering and physics, and graduated with a PhD from the California Institute of Technology in 1986. He loved using math and engineering principles to fold mind-blowing designs.

He wrote books on the subject, created more than 700 origami designs, invented the TreeMaker computer algorithm that helps others create origami sculptures and has seen his art showcased at museums around the world. In 2001, he quit his physicist day job working on lasers and semiconductors to focus solely on origami and hasn't looked back.

"Most people think that math and art are completely unrelated, very different, and express great surprise that someone could be mathematical and artistic," Mr Lang said.

Origami inspiration

At the MoMath show, his pieces include Dragonfly, which features a giant dragonfly on top of a vine, and Cyclomatus Metallifer, Opus 562, which is a large insect crawling over rocks.

It was Mr Lang's work and books that inspired Erik Demaine to pursue origami. Born in Halifax, Nova Scotia, Mr Demaine was a child prodigy, who was home-schooled until 12, earned a bachelor's degree in computer science and math from Dalhousie University at 15, got a PhD in computer science from the University of Waterloo at 20 and is now a professor of computer science at the Massachusetts Institute of Technology.

"I liked to do geometry but needed some unsolved problems to work on to challenge me," said Mr Demaine. And origami fit the bill. So he and his father, Martin, an artist in his own right, took up origami together and jointly created more than 300 origami sculptures.

Mr Demaine combined his math wizardry with his father's expertise in glassblowing art. "I would teach him mathematics and he would teach me how to make art," he said. Their origami art has been showcased at the Museum of Modern Art and the Smithsonian American Art Museum, among other galleries. Mr Demaine said he liked the way the worlds of art and math collided at the origami shows, attracting both art and math fans.

At the MoMath exhibit, some artists use other materials and fabrics, like snakeskin, ribbons, organza and even sterling silver to bring their art to life. The Demaines used linen in their Linen Swirls piece and poured hot blown glass onto wet paper for their Pyre artwork.

Ribbons, fashion and masks

Artist Faye Goldman used Japanese gold-edged polypropylene ribbons to create spheres, called 11 Hole Torus, Small Orange Egg and Small Pink Ovoid Egg, that look strikingly similar to glazed ceramic pieces - well, until you touch them or lift them up and realise they're made of ribbons.

Even fashion is part of the exhibit. Uyen Nguyen, an engineer-turned-artist, used origami designs to create skirts and a handbag. Instead of paper, she used vinyl, polyester, satin ribbon and cotton to make a 16-fold symmetrical skirt, and used a single piece of leather to create a foldable handbag. "It can fold down to a be a very tiny purse or it can expand up to be a very large bag - all using the techniques of origami and folding," Ms Lawrence, the museum director, said.

Then there's Joel Cooper's masks, which look like finely chiselled medieval faces that one might expect from a porcelain, metallic or papier-mâché mask. But he used paper and origami folding to create the masks and then added shellac, acrylic paint and polyurethane varnish to give them a final gothic appearance.

"Finding the right combinations of folds to create a shape is like finding the most elegant mathematical proof," Mr Cooper said in the comments next to the art.

Ms Lawrence said the origami show and the museum's interactive exhibits are all about inspiring visitors to ask how, why and what's next in the world of math. "It allows people to come in and see something beautiful, something artistic," she said. "And then to step back and say, 'Oh wait, there's math in this.'" NYTIMES

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