Ever wonder how origami artists create those amazing models of complex animals? Robert Lang can help you out. He’s a mathematician who’s been one of the pioneers in modern origami. His talk is titled “from flapping birds to space telescopes”. His point is that origami, which dates from before the 1700s in Japan, is no longer just about child’s play – it “has become a form of sculpture that involves folding.”
The key pioneer who made this happen was the Japanese folder Akira Yoshizawa, who not only created many new creations but invented a common language to describe origami. The more recent innovations have been based on math, and on learning from the past. Lang tells us, “the secret to productivity is letting dead people to your work for you” – if you can, find problems that someone else has solved.
At its root, every origami figure is a crease pattern. These figures follow some basic mathematical laws:
– They are two-color maps
– At any interior vertex, the number of mountains minus valleys equals 2
– When you look at the angles around a fold, the odd angles all add up to 180 degrees, as do all the even angles
– A sheet can never penetrate a fold
From those four laws, you can create any piece of origami. And you can build computer models to figure out how to create figures. To create a creature with many parts, you move from an idea, to a tree (a stick figure), a basic model and then the finished design. The hard part is getting from that stick figure to the model – it requires careful analysis to figure out how to create flaps in a model. It turns out that flaps need to be made from circles – they can be on corners, sides or the middle of a piece of paper, but creating flaps becomes the process of packing circles into a flat sheet. Using this principle, Lang has written a piece of software called “treemaker” which will turn a basic sketch into a crease pattern.
Some of the techniques used by modern origami designers are now proving useful to engineers, including aerospace engineers. Koryo Miura used an origami folding pattern to design a solar array that powered a Japanese space telescope that flew in 1995. Lang has worked with NASA on the foldable lens for a telescope, trying to figure out how to fold a 100 meter lens to a size that could be launched into space. The answer is an “umbrella pattern” that folds a circle into a compact cylinder. There’s a new heart stent designed with the fold patter we’ve all used to make little origami boxes – it allows the stent to travel through an artery, then expand to keep a vessel open. Origami, ultimately, may help save your life.