The Mathematics of Art

When you see the Eiffel Tower, or the Brooklyn Bridge, or the Gateway Arch, do you see a work of art? Or the successful completion of a particularly tricky math problem?

The 16 students in Murphy Waggoner’s May Term class may see both.

The class, “The Mathematics of Art,” meets one of the Quantitative Reasoning requirements and fulfills an arts requirement for the Engaged Citizenship Curriculum.

“This illustrates what is innovative about our new curriculum – that is, we embed skills like quantitative reasoning into courses, and many of our courses cross disciplines like this,” said Waggoner, chair of the Department of Mathematics.

At first glance, the class is attempting to bridge two fields that may not appear complementary. After all, isn’t math largely a left-brain activity, while art and creativity exist on the right side?

Let’s ask a math major.

“The class has taught me about patterns and different symmetry,” said Lauren Doocy, a freshman from Ankeny. “I learned a lot about that in high school geometry, but this is a totally different world for me.”

And now an art major.

“I realized there was symmetry in art,” said Sammie Moenning, a freshman from Evergreen, Colo. “But I didn’t know about the Fibonacci sequence and other sequences and ratios.”

Waggoner, chair of the Department of Mathematics, describes her class like this: “There’s a mix of students who are interested in art and wanted to fulfill their math requirement in an easy way. And some are interested in math and wanted to fulfill their art requirement in an easy way. And some who are actually interested in both, and a couple who don’t like either.”

Put them all together for a May Term, and what do you get?

An enormous Sierpinski Triangle Fractal constructed out of pennies – 2,187, to be exact (Waggoner supplied them.)

A fractal is a self-replicating image. A Sierpinksi Triangle is an enormous triangle that contains numerous other triangles within it.

Waggoner instructed her class to build a triangle with eight levels, or iterations, on the floor of the Carver Science Center’s atrium.

The work began at 9:10 a.m.

This is the first time Waggoner has asked her students to build the penny triangle. In the past, she has explored the relationship between mathematics and art by having the students sew a quilt.

One finished product now hangs in a classroom, with each block of the quilt representing a different math concept.

“For this project, the mathematics is that it grows exponentially,” she said. “But we also looked at the mathematics involved in a large installation.

“What are the things you need to consider to create a large installation of art? Space, time, money and, clearly, organization.”

Don’t forget the conflicts that can arise when students mostly interested in math work alongside students mostly interested in art.

“We had a little trouble,” Doocy said, laughing. “The art majors are saying as long as it looks right, it doesn’t matter how many pennies there are (in each triangle.) The math majors want the right number of pennies. We want it to be exact.”

The math majors prevailed. When the project was completed, at 10:27 a.m., Doocy was thrilled.

“I’m so excited, it looks so sweet,” she said.

Waggoner, too, was pleased.

“There has been so much collaboration and problem-solving in this,” she said.

Later this week, the students will present their final projects, which will feature everything from modular origami to brick-patterned sidewalks.

Zach Edler, a sophomore elementary education major from Clarence, said he wasn’t sure what to expect when the class began.

“At first, I wasn’t sure about it, because I’m not a very artsy person,” he said. “But I’ve really enjoyed it. It’s really made me see things differently. Anytime I see art now, I try to analyze it and look for the math inside.”

For his final project, Edler will create tessellations (patterns made from squares).

“I probably won’t be famous anytime soon,” he said.

Who knows? Even M.C. Escher, one of the math world’s favorite artists, had to start somewhere.


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