# Engineering principles revealed through ancient art

Goran Konjevod needs only a blank piece of paper to begin enlightening you about some basic principles of mathematics, science and engineering. Plus you could learn to make something kind of cool.

He uses the ancient art of origami – paper folding – to show students how intricate structures can be fashioned by folding paper into various patterns, and how the process demonstrates fundamentals of geometry and engineering design.

For one assignment, Konjevod, an assistant professor of computer science and engineering in the Ira A. Fulton School of Engineering, challenges students in his design course to use origami techniques to construct a paper model of a bridge.

The project teaches them rudiments of load-bearing capacity and structural stress, tension, resistance and curvature – important stuff to know if you have to design and build real bridges.

“I want them to see the mathematical aspects exhibited in the way materials behave, and to think like designers, to think how they would devise models to show what actually happens when you fold the paper in certain ways,” he says.

Konjevod’s combination of origami and mathematical modeling skills have recently brought him some recognition among his peers.

He won the first-place prize in the Exhibition of Mathematical Art at the 2009 national Joint Mathematics Meetings of the American Mathematical Society and Mathematical Association of America in Washington, D.C.

His work entitled Wave (see photo on this page) was selected from almost 5O works by 36 artists in the competition “for aesthetically pleasing works that combine mathematics and art.”

The award was established in 2008 through an endowment from an anonymous donor who wanted acknowledgement of works “that demonstrate the beauty and elegance of mathematics expressed in visual form,” according to the American Mathematical Society.

Konjevod’s Wave is an example of “pleat tessellation.” It’s made through a series of parallel folds, or pleats, formed into a Z-shape, creating a layering effect that triggers a structural tension. The tension produces a curvature that gives the piece its three-dimensional shape.

A tessellation is a mathematical term for tiling. Think of a flat surface divided into smaller parts, all of equal shape. (See the well-known graphic art work of M.C. Escher for an example of tessellations.)

Wave is one example of how origami exhibits the way simplicity and complexity can coexist in the world of design, mathematics, engineering and science.

But the lessons learned from origami have vital practical applications, Konjevod says. Understanding how to shape materials to produce specific kinds of folding and layering capabilities has led to technological advances.

Stents are one example. They are the tiny devices that can be folded up and inserted into blood vessels, and then made to unfold and push open the vessels to help restore lost blood circulation.

Similar mechanics are at work in technology that allows us to transport a large telescope into space, making it compact for travel by folding it up, and then unfolding it in space to unveil its lenses and let it do its work.

Konjevod says the wonders of origami also bring up some questions that scientists and engineers are still trying to answer, such as the workings of a phenomenon called protein folding.

“Proteins can fold themselves into shapes that are complicated. We don’t fully understand how they do it,” he says. “What are the physical rules that guide this folding? It’s something nature does on it own, yet we don’t have an equation to explain how this happens so that we could replicate it.”

It’s sort of the same with origami. We know what can be done by folding paper, we just don’t completely understand how the paper does what it does.

“It’s a real computer science challenge,” Konjevod says. “I would love to write a computer program that solves the mystery of how to model what paper will do when you fold it in specific ways.”

See more of Konjevod’s work at Organic Origami.