Why is the ancient art of origami so useful for engineering? In this episode of Veritasium, Derek Muller visits with origami artist Dr. Robert Lang and mechanical engineering Professor Larry Howell to learn more about how origami and engineering are coming together to create solutions for new technologies. From Veritasium:

On first glance it’s surprising that origami — a centuries old art of folding paper to achieve particular aesthetics — is applicable to engineering. But upon closer consideration there are a lot of reasons methods developed for paper folding are also applicable to engineering: origami allows you to take a flat sheet of material and convert it to almost any shape only by folding. Plus for large flat structures, origami provides a way of shrinking dimensions while ensuring simply deployment – this is particularly useful for solar arrays in space applications. Furthermore, motions designed to take advantage of the flexibility of paper can also be used to form compliant mechanisms for engineering like the kaleidocycle. Since the principles of origami are scalable, mechanisms can also be dramatically miniaturized.

Lang gives credit to Japanese “grandmaster of origami” Akira Yoshizawa for modern breakthroughs in the art. “His work inspired a worldwide renaissance of origami creativity.”

Lang also describes the geometric thinking behind how original origami designs are created. Example: How did he invent this origami potted cactus full of spines from one large uncut square of red and green paper? “The math comes down to a way of representing a design called a crease pattern…”

It’s a plan for how to fold… in this case, how to fold a scorpion. A really good way of designing something like this is to represent every feature—claw, leg, tail—by a circular shape. It’s not circular folds, it’s an abstract concept that you represent the pattern by a circle, but then you find an arrangement of those circles on the square, like packing balls into a box…

The arrangement of those circles tells you the skeleton of the crease pattern. And from that, you can geometrically construct all the crease patterns. You follow rules… it’s all step by step: ‘If you find this geometric pattern, that tells you where to find the next line.’ You go through that process until you’ve constructed all the lines.

And when you’re done, you can take away the circles—they were the scaffolding for the pattern—and the pattern of lines that’s left are the folds you need to create the shape…

And this was probably the biggest revolution in the world of origami design: If you follow that systematic process, the fold pattern would give you the exact pattern you set out to fold to begin with.

Watch this video next: The Sphere-Packing Problem.

Related research: The Miura Fold and this Tessellation and Miura Folds DIY project from Science Friday.

Plus, watch more videos about origami on TKSST, including The Kresling-Pattern and our origami world, this mini origami robot self-folds, performs tasks, & can be dissolved, how to make a hexaflexagon, and Robert Lang’s Incredible Origami Creations: A Fold Apart.