Lion's Eye Favorite: From Origami to Calculus

July 6, 2009

Students applying origami principles in Calculus class

"He was brilliant!" said Forest '10 about the recent visit of Dr. Thomas Hull, author of Project Origami, Activities for Exploring Mathematics and associate professor of mathematics at Western New England College.

Hull instructs a Calculus class after assemblyHull started assembly with a quick-paced, hands-on project. "Draw a dot in the middle of the paper," Hull instructed, as Exeter's 1,000 students picked up the 4-inch sheets that had been placed on Assembly Hall seats. "Now fold through the dot, any fold you want." After a few seconds, he added: "Now fold through the dot again. If you're feeling adventurous, make another fold. And again, as many times as you want."

"Now, unfold the paper," Hull continued. The students observed a series of "valleys" (dips) and "mountains" (peaks). "Now, label the mountains and valleys, count the number of each, and shout out your results." Students eagerly yelled out. Hull noted the numbers on a projector. Soon, everyone recognized a pattern.

Before you could count to 5 (or make another crease), Hull was citing the theorem that proves the results – "Maekawa's theorem":

The difference between the number of mountain folds and valley folds is always 2.

From paper folds to mathematical theorems in under 5 minutes, the students were hooked and eager for more.

Students experiment with paper folding"It's cool!" was Hull's refrain, as he walked Assembly Hall through more origami-based math challenges. "Proof by monorail," for example, encouraged students to visualize themselves as a monorail speeding along the edge of folds and angles to determine polygon angle values. 

Hull's presentation culminated with a rapid-fire tour of real-world, origami-based applications. They ran the gamut from the mundane – Tokyo's large subway map which folds to a tiny 3x4 inches – to way-out-there breakthroughs – a Hubble Telescope prototype for a massive folding lens.

After assembly, Hull visited two math classes: Philip Mallinson's Calculus and Jeff Ibbotson's Advanced Integrated Mathematics. Forest, a calculus student who "likes math most when it can be applied to physical and concrete ideas," loved the fun of the in-class lesson, and the challenge. He found that Hull "put a totally different spin on" calculus.

"We learned how to use origami to understand the concepts of a parabola," explains Forest. "Dr. Hull showed us that many folds tangent to a parabola turned into a representation of a curve. And then we proved that the curve was a parabola . . . It's a really interesting approach to getting a better understanding of concepts, although keeping up with Dr. Hull is not easy, even after 3 years of high school algebra and geometry."

Hull has visited Exeter before, when he presented at the Anja S. Greer Conference on Secondary School Mathematics, Science and Technology in 2007.

Interested in learning more?

Learn more about Exeter's Math Department…

For more information on origami and math, see Hull's website…

Read about Exeter's Anja S. Greer Conference on Secondary School Mathematics, Science and Technology, coming up this June...

Check out the Exeter Math Institute, a one-week professional development program for public middle and secondary school mathematics teachers…

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 Lion's Note: This story first appeared on April 14, 2009.