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Mathematics Takes Shape with Geometric Sculpture

Jun 05, 2017


Math students around geometric sculptureThis spring, students in Professor Eve Torrence's Art of Mathematics course learned that some artists use mathematics as inspiration to create works that explore mathematical concepts. An end-of-semester project gave students the opportunity to do the same as they built a six-foot diameter geometric sculpture out of cardboard.

The abstract geometric sculpture, known as Twenty-Twenty, was designed by Professor George Hart of Stony Brook University and is based on a shape called the compound of five cubes.

"It is an abstraction of that shape that uses many intersection points and lines in the design," explains Torrence. "The design is quite complex. George Hart's designs are very clever and mathematically interesting."

New Perspectives
Torrence says her goal for the Art of Mathematics course is to use art to expose students to areas of mathematics they have not seen before. The course begins with a mathematical study of perspective, and students learn to make perspective drawings.

"After that we move from two dimensions into three dimensions and learn about polyhedra and the design of sculptures like Twenty-Twenty, which are based on geometric shapes," she explains. "We study interesting areas of mathematics like the fourth dimension, fractal geometry, topology, and combinatorics. These are advanced topics that math majors may not see until graduate school. But this is a general math course for all students. I’ve had students take the class who are majoring in disciplines across the board—including fine arts, art history, and other humanities. Through art I am able to expose them to these advanced topics in a way that they can understand and appreciate the relevance and power of abstract mathematics."

The 16 students met in the Cobb Theatre shop and used power tools to cut 60 identical shapes out of stacks of cardboard. They assembled the sculpture in the McGraw-Page Library, where it was on display for Research Day, which took place May 12, 2017.

A Versatile Subject
Emma Tiernan '19, an engineering physics and chemistry major, emailed Torrence shortly after the semester ended.

"I want to thank you for teaching such an interesting math class," wrote Tiernan, a member of Macon Women Engineers. "Your class reminded me why mathematics is such an interesting and versatile subject. This class has actually helped me in engineering and organic chemistry, because I am now able to visualize three-dimensional problems."

Torrence says, "It was exciting for me to hear that the course was helpful to Emma in her engineering and chemistry courses. This is an outcome of the course that I had never considered and shows how a liberal arts education gives students different perspectives on their major area of study."

Eve Torrence
Torrence joined the R-MC faculty in 1994. She served as president of Pi Mu Epsilon (PME), the National Mathematics Honor Society, from 2011 to 2014, and has served on the national council of PME since 2002. She has also served as chair of the Maryland/District of Columbia/Virginia section of the Mathematical Association of America (MAA) and as chair of the Committee on the Faculty at Randolph-Macon College.

Torrence is the author of Cut and Assemble Icosahedra: Twelve Models in White and Color and, with Mathematics Professor Bruce Torrence, The Student's Introduction to Mathematica: A Handbook for Precalculus, Calculus, and Linear Algebra. She is also a co-recipient, with R-MC Mathematics Professor Adrian Rice, of the 2007 Trevor Evans Award for exceptional writing published in the MAA journal Math Horizons.

Torrence earned her B.A. magna cum laude from Tufts University and her M.A. and Ph.D. from the University of Virginia. Her work has been displayed in the college's McGraw-Page Library as well as at international juried shows of mathematical art at the annual Joint Mathematics Meetings.

In 2013, Torrence was chosen to be one of 12 recipients of the 2013 SCHEV/Dominion Resources Outstanding Faculty Award (OFA), the Commonwealth's highest honor for faculty at Virginia's public and private colleges and universities.

In 2015 she won the top award in the International Juried Mathematical Art Show at the Bridges Math and Art conference in Baltimore, Maryland. Torrence's aluminum origami sculpture, "Sunrise," hangs from the ceiling in the lobby of R-MC's Copley Science Center. Torrence is a member of the board of the Bridges Organization, which sponsors the annual Bridges Math and Art conference.