Math Society Considers Hyperbolic Coral Reef

A workshop and talk during last week's Mathematical Society of America meeting at VMI discussed the Hyperbolic Crochet Coral Reef. -- VMI Photo by Julie Rivera.

LEXINGTON, Va., Oct. 29, 2012 – A project that melds the seemingly disparate realms of art, upper-level math, and environmental awareness was the topic of a talk given Friday, Oct. 26, at VMI as part of the fall meeting of the Maryland-D.C.-Virginia section of the Mathematical Society of America.

Caren Diefenderfer, a professor at Hollins University, and Jan Minton, a professor at Roanoke College, gave a joint presentation entitled “Hyperbolic Crochet Coral Reef Comes to Southwest Virginia.” As its name suggests, the reef is a handmade, crocheted model of a coral reef, complete with the complex shapes and riotous panoply of color found in a real underwater reef. Making the reef mathematical is its fidelity to hyperbolic geometry, a field of geometry that explores curved lines.

Hyperbolic geometry is the least well-known of the three geometric fields, the other two being Euclidean or plane geometry, the type taught in high school, and spherical geometry.

“Basically, non-Euclidean geometry is throwing away the idea that two parallel lines never intersect,” explained Maj. Nate Axvig, assistant professor of math at VMI. “In a hyperbolic space, the distance on a point between two parallel lines can increase.”

In her remarks, Diefenderfer invited her audience of 125 math professors and students to visualize the hyperbolic plane as curved like a Pringles potato chip.

In 1997, efforts to model hyperbolic geometry took a giant step forward when Dr. Daina Taimina, a math professor at Cornell University, discovered that crochet produced an authentic representation of hyperbolic space. The world’s first hyperbolic crochet coral reef came into existence in 2005 when sisters Margaret and Christine Wertheim created one in their Los Angeles living room. The Australian-born duo, one a science writer and one an artist, began the project to call attention to the plight of their home country’s Great Barrier Reef, whose existence is being threatened by global warming.

The Wertheim sisters’ coral reef eventually attracted national attention in the form of an exhibit at the Smithsonian – and Minton, a longtime crocheter, was one of the visitors. Upon returning to Roanoke, she immediately launched the creation of a satellite reef, one of many now either completed or under way around the world. Diefenderfer joined the project while she was on sabbatical from Hollins last year.

Altogether, more than 100 people have worked on the Roanoke Valley Reef since its inception in September 2011. With the project now nearing completion, an exhibition at Roanoke College’s Olin Gallery has been scheduled for Jan. 25-March 1, 2013. A complementary, marine-based exhibition, “Echo Sounding,” will run at Hollins’ Eleanor D. Wilson Museum Jan. 10-March 2, 2013.

Minton said that she hopes visitors to the Roanoke College exhibition will leave “with an awareness of the plight of coral reefs and some understanding that there’s a mathematical aspect to these shapes you see quite often.”

Diefenderfer added, “The real mathematical issue is that it’s a pattern. Patterns are everywhere. By observing these patterns, you learn an incredible amount of mathematics.”

VMI’s Axvig likewise echoed the educational possibilities of the hyperbolic crochet coral reef. “We need to raise mathematical awareness,” he said. “A lot of people, they think that [math teachers] sit around and add numbers together. They think that math is something that’s completely figured out, and it’s not. There are still are questions that we’re still investigating. There’s a lot we don’t know.”

Also making a presentation during the meeting was Maj. Randy Cone, director of VMI’s Math Education and Resource Center, who moderated a forum on the status of mathematics education.

–Mary Price