Editors’ Note: This feature appears as it was published in the spring 2017 edition of UT Dallas Magazine. Titles or faculty members listed may have changed since that time.

Innovative programs. Remarkable teaching and research. Alumni successes. All of these factors add up to a continuing appreciation for mathematics at UT Dallas. Some interesting applications of the discipline are showcased here.

Geometry Threaded Through Art

GABRIEL DAWE MFA’11 creates beauty by combining the Pythagorean theorem with up to 60 miles of thread.

Gabriel Dawe MFA’11

Gabriel Dawe was doing work at the University’s artists residency when he was invited to collaborate with an architect to explore the links between fashion and architecture for an upcoming show.

Dawe, who had been working with embroidery and textiles for years, saw an opportunity to think big. “I wondered what would happen if I used the core material of clothing — thread — at the scale of architecture,” he recalls.

That idea led him to develop an installation consisting of large intersecting triangles of thread that seemed to curve and undulate in open space, shifting with the viewer’s perspective and the lighting. It looked as ethereal as a spider’s web but had a geometrical structure that gave it stability.

While the results of his efforts were striking, the process of creating the installation proved to be exceptionally demanding. In addition to the grind of calculating the distance of every triangle leg and hypotenuse, Dawe had to climb up and down a ladder to place each thread with pinpoint precision. “I was working almost seven days a week for five weeks,” he recalls. “It was really tough on the knees.”

But the breathtaking project proved to be so popular that he’s been pursuing variations on the theme ever since. He’s constantly looking for new ways to improve the work by creating ever-more pleasing symmetry and integrating other mathematical concepts like the Fibonacci sequence. “Mathematicians often talk about finding ‘elegant’ solutions to problems, and I relate to that,” says Dawe. “I’m always trying to find ways to make something a little more perfect.”

A Better Cancer Test

The statistical modeling of DR. SWATI BISWAS, associate professor, is helping guide patients with a high risk of breast cancer in crucial and timely management of their condition.

Dr. Swati Biswas

The Brewer’s Formula for Success

Lawyer-turned-craft-brewer MICHAEL PETICOLAS BA’95 shares the delicate mathematical balance that led to award-winning beers.

Michael Peticolas BA’95

 

Michael Peticolas spent years dreaming of starting his own brewery as he toiled as a Dallas-based trial attorney. And in 2010, he wrote a business plan that would help him do just that.

As testament to his methodical nature, he developed the brewery business plan a year before he brewed his very first commercial batch of beer. The recipe he developed is now known as Velvet Hammer, the flagship beer for Peticolas Brewing.

While there were plenty of numbers in that business plan, Peticolas says the real math of a brewery comes in recipe development. “I went to the American Brewers Guild and took their intensive brewing science and engineering course,” he says. “There’s quite a bit of math in that. It helped me scale up from 5 gallons that I was doing in my backyard to the 500 gallons I brew at a time today.”

The challenge of recipe formulation comes from the almost infinite number of variables that can instantaneously transform a beer from exceptional to undrinkable. “Will you use kilned malted barley or roasted barley? How much sugar do you want to extract from the malted barley? How much alcohol do you want to end up with?” he says, ticking off just a few pieces of the equation. “There are only four ingredients in beer — water, malted barley, hops and yeast — but there’s so much that’s going on in the context of recipe development.”

Peticolas seems to have found the right answer: His brewery’s beers have earned two gold medals from the Great American Beer Festival, the biggest award in the beer industry. “There are a lot of things that go into making a superior beer,” he says. “But getting the initial formula right before you move forward is of the utmost importance.”

Object Lessons

DR. JOHN ZWECK, professor of mathematics, adds a new dimension to mathematical education to help students learn difficult concepts.

Dr. John Zweck knows that many of his calculus students will go on to become engineers or biochemists — people whose work will come to life in the material world.

Yet for years, his teaching rarely left the page. He relied on two-dimensional models printed on textbook pages to describe important geometrical shapes like saddle surfaces. But no matter how beautifully rendered, these drawings were often confusing to students — and it sometimes caused them to give up before they’d even started. “If you’re trying to have a conversation about what is represented by specific formulas, the representations that a student and a professor have in their heads have to line up,” he says. “Otherwise, we’re just talking gobbledygook.”

It was as he was pondering this problem a few years ago that Zweck began hearing about 3-D printers, and he immediately saw opportunity. With a small grant from the National Science Foundation, he created three-dimensional printed models of saddle surfaces and helices, among other shapes. Now, Zweck brings dozens of these models to his classrooms to help students understand the work they’re doing on a real-world level. “It’s different when you can put a helix right in front of your nose or draw your finger along the curve,” he explains.

The bigger idea? He wants these models to help students develop a more nuanced understanding of mathematics. “When students learn to use verbal explanations to connect logical thinking, geometric imagination skills, and algebraic calculations, they become creative problem solvers [in the discipline],” says Zweck.

The Tiny Tells of a Great Big World

Mathematics professor DR. SUSAN MINKOFF’s work identifying trace gases may save lives.

A tiny amount of ammonia in your breath could signal the onset of liver disease. A whiff of certain chemical compounds at the airport could indicate the presence of a bomb. Too much carbon dioxide might mean a car won’t pass a required emissions test. The number of applications for sensors that can detect trace gases, says Dr. Susan Minkoff, is nearly endless.

But while the need is great, building those sensors turns out to be a trickier task. The mathematics professor works with colleagues from around the country to develop computer-generated models that predict how the sensors will behave in different situations. For example, many gases will absorb the energy of a specially tuned quantum cascade laser, which then causes the molecules to vibrate. With a tiny tuning fork, these vibrations can be detected and amplified. “When we’re trying to detect really small amounts of gases, parts per million — or even just a few parts per billion — we want to determine the best tuning fork geometry to maximize the signal,” Minkoff explains.

A simulation to one set of tuning fork tines, for example, led to a signal that was more than 20 times stronger — and opened up new opportunities for creating a cheaper sensor. Because the sensor may ultimately be used in the auto industry to detect certain emissions, that potential savings is critical.

The melding of math and real-world applications is work that Minkoff finds invigorating. “Solving equations on paper is fun, but the real world is messy and complicated,” she says. “We want to make sure that we can help develop models that are as close to reality as possible.”

Swimming in Numbers

English Channel swimmer SOPHIE RUTENBAR BA’06 relies on math to improve her performance.