Peace Flight
Robert J. Lang and Kevin Box
Folded 2013; Composed 2013
cast stainless steel on stone; approx. 3′ x 2′ x 4′ on stone
© Robert Lang

A Creative Process Governed by Math

Dr. Robert Lang can make paper cranes. But his origami cranes not only have feathered wings and three toes on each foot, they soar with life.

Origami artist Robert Lang
© Robert Lang

In 2001, this physicist/engineer left his successful science career to write a book about how to make your own designs for origami, the traditional Japanese art of folding paper.

Why the career change?

This obviously brilliant man, who has 50 patents awarded and pending on semiconductor lasers, optics, and integrated optoelectronics, had an “Oh, I see” moment:

There were plenty of other really good engineers and managers that could do whatever I could do as an engineer, but I felt like there were few people who could write this book. 

So he took a risk, left his job, and decided to see where it would take him.

Millions of folds later, he has found that origami continues to take him beyond what he could have imagined.

Koi, opus 425
Folded: 2002; Composed: 2002
One uncut square; 15″
© Robert Lang

Lang’s work has appeared worldwide in both ads and art shows.

He works in the more traditional smaller origami size as well as life-size. He even works in currency. While much of his work is made from some sort of paper, he has collaborated with sculptor Kevin Box to render a number of his pieces in metal.

Dollar Camera
Folded: 2009; Composed: 2009
Two uncut one-dollar bills; 3″
© Robert Lang

The Math

When he switched careers, Lang admits at first he was worried that giving up engineering would mean giving up the mathematical work he loved so much. But, he says:

The math of origami is as interesting as engineering ever had been. The itch [to work with math] gets scratched as much by origami as it ever did by physics.

To make an origami figure, Lang goes through four steps:

• He starts with the subject.
• Then, he draws a tree figure (like a stick figure) of the basic shape.
• Next, he creates a folded-paper base with flaps for the appendages.
• Finally, he forms the specific shape into the model.

Four-step process for origami design
© Robert Lang

The tree figure and the final shape are the easy parts. Creating the base is the hard part. That’s where math comes in.

The math of origami is about shapes and relationships and forms, not necessarily arithmetic. The folding pattern to create a flap (or leg or antennae) is based on a circle pattern. The smaller the flap, the smaller the circle (a quarter circle is the smallest amount of paper you need to make a flap).

If you know how to “pack” these circles, which represent the body parts, and fill the remaining paper with a mathematical crease pattern, you have an origami pattern—and have solved another math challenge.

Stag Beetle BP, opus 477
Folded: 2005; Composed: 2005
One uncut square of Origamido paper; 5″
© Robert Lang

Solving Puzzles

A passionate scientist, Lang sees every origami design as a puzzle to be solved, especially the ones he does for artistic purposes.

His deep plunge into understanding the math behind his work has helped him create figures one could never imagine would evolve from a single flat piece of paper. Lang explains:

What is possible in origami is defined by the mathematical properties of a folded sheet of paper; if you understand the math, you can use it to create a lot of forms that you probably wouldn’t have discovered just by intuition.

Sure, there are some challenging projects Lang has begun that are not done yet. And that’s how he sees it—they aren’t failures; they are just not done yet. He feels that nothing is impossible since he is always learning new techniques and approaches.

Siam
by Robert J. Lang and Kevin Box
Folded: 2012; Composed: 2002
cast bronze, silver nitrate patina; 10″ x 8″ x 6″
Selby Fleetwood Gallery
© Robert Lang

What’s the Point?

Origami is wondrous, but it’s also useful. Lang explains:

Problems that you solve to create something beautiful turn out to have an application in the real world.

Scientists needed to get a football-field-sized lens into space, but it had to be carried on a spacecraft. What inspired their design? Origami.

Doctors had the idea of placing a stent in a human artery, but it had to be tiny to get to its destination. What inspired their design? Origami.

Squaring the Circle, opus 596
Folded: 2009; Composed: 2006
One uncut irregular sheet of Japanese paper; 12″
© Robert Lang

Engineers wanted to put inflatable, expanding air bags in cars for emergencies. What inspired their design? You get the idea. . .

Sharing the Lessons

Lang seems to be as passionate about teaching origami technique as he is about creating the designs. A natural teacher, Lang makes the math behind folding circle patterns to create flaps simple and logical, as illustrated in this TEDtalk.

Why the interest in teaching? His response is a perfect reflection of his precise art: there is a satisfaction in delivering a well-crafted presentation.

But he also reflects,

Maybe it’s because when I discover something, the ah-ha moment is really fun—that moment when you’ve discovered something new is a rush. When I see it in someone else’s face, I am vicariously experiencing it by seeing it in them.

Oh, I see, Dr. Lang. And we at OIC couldn’t agree more!

Robert Lang provides folding patterns for a number of his pieces on his site. Get additional guidance from Origami Instructions and find free download patterns from Origami USA.

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