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Courtesy of Jiangmei Wu, Folded Light Art + Design

STANDARDS

CCSS: 7.G.B.5, MP7, MP8

TEKS: 6.8A, 7.11A, 7.11C

Bringing Math Into The Fold

A traveling exhibit uncovers the math behind the art of origami

Courtesy of Robert J. Lang Origami

Simply folding paper can lead to amazing creations—from paper cranes that fit in the palm of your hand to room-sized sculptures. Origami is an ancient art form, but origami artists are also applying geometry with each fold.

“Origami is a combination of art, science, and mathematics,” says Paul Jackson. “Math underpins everything.” Jackson is one of nine artists from around the world whose creations are on display in a traveling art exhibit called “Above the Fold.” For the exhibit, each artist used his or her personal technique to create original origami pieces. Jackson, for example, folded large photographs of his hands to create collages. He wants viewers to think about the role hands play in creating origami.

Courtesy of Robert J. Lang Origami

Other sculptures in the exhibit use mathematical curves, triangles, and tiling. Ruga Swan by Jiangmei Wu is a series of large connected parallelograms that curve into a spiral. “I use simple rules of geometry to do this pattern,” says Wu. The entire piece resembles the wings of a swan, filling the room so visitors can walk through the sculpture to get different perspectives. “It’s pretty amazing what you can do with fixed, folded patterns,” she says.

Robert Lang is a former NASA scientist who is also a master origami artist. He creates everything from intricately folded animals and flowers to complex geometric figures that show mathematical principles at work. His original design for a Japanese samurai helmet beetle requires more than 300 steps to complete! Lang even considers the flat, unfolded origami paper as its own kind of art.

“Above the Fold” has been touring museums around the U.S. since January 2015. It’s now on display in Delray Beach, Florida, and then moves on to Allentown, Pennsylvania, in March. This modern take on an ancient art pushes the limits of what a simple piece of paper can be. “Origami isn’t just little birds and butterflies,” says Jackson. “I think people have realized there is a maturation of origami.”

Use the interior angles formula and the crease pattern below to answer the questions. Angles marked with slashes are congruent.

A. How many sides does the green polygon have?

B. What is the sum of the angles in that polygon?

There are many triangles inside the crease pattern. What is the sum of the angles in any triangle? 

Find the measures of these angles in the diagram:

            ∠ A                    ∠ D

            ∠ B                    ∠ E

            ∠ C

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