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Insects, Circle Packing, and the Math that Underlies the Art

As I’ve said here before, I’m fascinated by how artists put math to work. Part of this interest stems from my own experience as the daughter of an engineer who majored in art; and part from hearing my son say something to the effect of “why do I need to take math – I’m going to be an artist/animator/cartoonist/you get the idea.”

math-learning-snacks-insectsSo when I heard Robert Lang’s TED talk “Idea + Square = Origami” I found beauty in the way he uncovers the mathematical principles of this traditional art form and puts them to work. Origami is 1 uncut square and folding. He (and others) are modernizing the art, using math and engineering to fold intricate designs that are delightful, intriguing, and sometimes, as it turns out, very useful.

Robert Lang is a physicist, using the tools of physics and engineering to break down problems and study the underlying theory. Provocatively, he says the secret is letting dead people do your work for you. You take your problem, turn it into a problem that other people have solved before you, and let them solve it for you – you use their solution.

The 1st step to modernizing this art was the development, by a Japanese artist, of a language of dots, dashes and arrows that can be used to describe the design of a form. Traditionally a sheet is folded in half repeatedly to make a flap, to create the leg of a beetle for example. The crease patterns when it’s unfolded reveal a quarter circle – you need a quarter circle of paper to make a flap. You can also make flaps from other parts of the paper, but a flap needs some part of a circle. If you want to make a figure with a lot of flaps, you need a lot of circles. Origami artists discovered in the 90’s that they could make very complex designs by packing more circles into a single sheet of paper. The basic rules of origami are simple, but these artists were able to create intricate designs by understanding these rules and pushing them further.

Math learning and the rules of origami

As with so much else in our lives now, computers have extended what this art form can do. Lang developed a program, based on these simple rules, that can calculate the crease patterns and do the circle packing. Origami, once the preserve of a few select, skilled artists, was revolutionized by understanding the mathematical principles underlying it and writing software to do the number crunching.

Lang goes on to provide wonderful examples of how origami has now been made useful in the real world, with applications in medicine, science, space, consumer electronics, and more. It’s used to allow things that need to be big and sheet-like when they arrive at their destination to be folded down to a compact form to make their journey – like the lens for a hundred-meter telescope used in space.

Here’s a wonderful perspective on all of this. Robert Lang said, wrapping up his talk, “When you get math involved problems that you solve for aesthetic value only, or to create something beautiful… it may turn out to have an application in the real world. And as weird and surprising as it may sound, origami may someday even save a life.”

You can learn more about it in Lang’s book “Origami Design Secrets: Mathematical Methods for an Ancient Art.”