Aquinas College’s classrooms are filled with exciting learning opportunities, challenging students to expand their current knowledge-set and test new theories, respond to relevant ideas, and develop comprehensive worldviews. However, Aquinas students often take their education beyond classes, exams, and papers, into deeper realms of study.

One of the ways in which they can do so is through the Mohler-Thompson Summer Research Grant, and other opportunities which finance student research projects into exciting fields of study. Just ask Megan Ternes, third-year Aquinas student (Mathematics and German double-major) and mathematics researcher, whose investigation of hyperbolic geometry has led to an exciting publishing opportunity.

In the summer of 2011, Ternes and Dr. Mike McDaniel of the AQ mathematics department began their first forays into studying hyperbolic geometry. At that time, McDaniel explained, “When we get five or six more new properties, we will have enough for a paper.” They continued their work together - often sharing their findings via a Wikispaces page which allowed them to work at a distance during the summer, pulling together a variety of ideas, until the time came for the paper to be written. The pair had studied a relatively newer form of geometry, yet now would come the challenging part: synthesizing this information in academic form to be analyzed by others.

Following the paper’s completion, Ternes explained the research process: “Dr. McDaniel actually asked me after class one day, what I was doing and if I would be interested.” She had never done formal research prior to that day, nor was she familiar with this particular form of geometry prior to her work with McDaniel. “I said, ‘Cool! Teach me, because I have no idea what this is, but okay - I can learn. Sure!’”

“A lot of the days we would meet at the library or at his office, and just work in the same area. Then later in the summer - June-ish - once we had a bunch of our stuff done... I would keep writing. At that point we were starting to write the paper. We were putting everything on a Wikispaces page. So we could both have an online login, and post anything that we had done.” Ternes said the online element made the research go more smoothly and helped to keep each part of the research coordinated with all others.

“It happens a lot in math that when you have something that is a truth, a lot of times the support for it is interesting,” McDaniel said of the research. “And it’s finding that support that’s the tough part: ‘Why is this true all the time?’ It’s very difficult to do sometimes.” Of the challenges of the research itself, Ternes said, “It wasn’t too bad. I felt like I picked up on all the rules of the geometry fairly easy. Obviously, we had to prove the stuff that we found. Proofs have never been my strong point.”

McDaniel, however, is highly complementary of his co-researcher’s ability and work-ethic: “With Megan, she’s one of these people that just keeps coming up with diamonds. There are people that are sometimes referred to as ‘idea hamsters,’ where they just spew out ideas, and they just come up with these things. And I think she is a potential math idea hamster.” Ternes reciprocated McDaniel’s positive feelings, saying of the professor, “I think he’s funny, and great to work with.”

The next step is the submission of the paper for publication. At the moment, the paper is undergoing preparation, reviews, and edits. Responses have thus far been positive, and both McDaniel and Ternes anticipate its eventual publication (ideally in the publication’s fall issue). The build-up is exciting, but this research team is already anticipating future work together, given that they work so well as a team.

“[Megan] has a very good instinct for finding interesting math ideas,” McDaniel said. “Usually, I have to come up with stuff. She came up with stuff on her own, and that was very cool. I like working with her. I would work with her again in a heartbeat.”