The Beauty A NEW VIEW OF MATH
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“You don’t have to be a poet laureate to appreciate a poem and you don’t have to be a mathematician to appreciate some math.” - D R. S EA N LAWTO N Assistant Professor of Math
Where some people see math as a string of numbers, Dr. Sean Lawton sees art. His tools of captivating others to recognize math’s beauty are novel. Lawton uses crochet hooks, skeins of yarn and a lesson on crocheting that enables people to better learn and appreciate the math in our world. “I’m trying to motivate the people who are scared of math completely. I’m trying to get people to recognize that there is more to it than they thought and that they are capable of doing it and that it is interesting,” said Lawton, assistant professor of mathematics. “You don’t have to be a poet laureate to appreciate a poem and you don’t have to be a mathematician to appreciate some math.” Lawton initiated the Hyperbolic Crochet Project last year as one of the first outreach activities in the Experimental Algebra and Geometry Lab (EAGL) he founded when he came to UTPA in 2009. Since then, Lawton and his student assistants have traveled to numerous area middle and high schools, as well as museums and libraries, to provide a different perspective of math. The hundreds of crocheted exotic-looking creatures that have been created in a myriad of colors, sizes and degrees of floppiness (curvature) as a result of the project are models of the hyperbolic plane - a non-Euclidean form of geometry discovered in
by Gail Fagan the early 1800s. Models of the hyperbolic plane have shapes with negative curvature similar to a horse saddle or a Pringles potato chip. In nature, hyperbolic forms can be seen in the curly edges of kale or in the shapes of sea slugs and some types of coral. However, a durable, tangible representation of a hyperbolic geometric model didn’t come about until 1997. That’s when Daina Taimina, a researcher from Cornell University and an experienced crocheter, devised a crochet pattern for a model that put the advanced mathematics concepts of hyperbolic geometry readily in the hands of researchers as well as students to study. Lawton based the EAGL’s project on Taimina’s model, which he says encourages conversation while crocheting and a sense of fun about learning. “We are trying to make these ideas more accessible to a larger audience. This is one of the mechanisms we are using to motivate and inspire,” Lawton said. Lawton’s lab assistant Jesus Chavez, a freshman majoring in computer engineering, helps students with the algorithm the crochet pattern is based on as they begin their models. Chavez thinks Lawton’s project is an innovative method of creating greater interest in math. “Personally, I wasn’t even aware of such applications until I became involved with this project, now I ‘see’ hyperbolic geometry everywhere!” he said. While the lab primarily focuses on outreach, EAGL also supports undergraduate research in pure and applied mathematics. It is affiliated with similar labs at the University of IllinoisChampaign/Urbana and the University of Maryland-College Park, where Lawton earned his bachelor’s, master’s and Ph.D. in math. To learn more about the project, visit the Experimental Algebra and Geometry Lab at http://eagl.wikidot.com/.