Taking a different Trangle on Train Tracks

Everyone learns basic principles of math, which include addition, subtraction, multiplying, and division. However, math becomes more complicated once people move to the next grade. Many people feel discouraged when math gets tough, but Rebeca Bowen and Julia Graham didn’t back down from presenting “Trangles and Train Tracks” at the 2020 Piedmont Symposium.

“As a beginning researcher, it’s nice to work on something original, but yet closely related to your advisor’s research,” said Rebecca Bowen, senior mathematics major at Piedmont College. “I really fell in love with this topic.”

Bowen proved that Trangles are equivalent to polyhexes, which is an assemblage of regular hexagons with adjoining sides. Graham discovered how train tracks work but breaking it down to its purest form.

 “The main problem I encountered was trying to come up with conjectures or proofs, because train tracks have not to my knowledge been researched, so there was a lot that was unknown,” said Julia Graham, senior physics major at Piedmont College.

Having the drive to push through and explain a topic that would leave many clueless can be stressful, but they got plenty of help from their professor Dr. Torrance.

“Of course, Dr. Torrance helped a lot with the formulation of the proof, but it’s a spectacular feeling to prove something that nobody’s ever proven before,” she said.

The complex topic was born once Dr. Torrance and his son were building toy train tracks and then continued to do further research. Once he developed more questions for his capstone students, he was excited to give them the task to do their research.  

“Working one-on-one with students on interesting math problems is hands down my favorite part of my job. Seeing how they tackled these problems was exciting” said Dr. Torrance, assistant professor of mathematics at Piedmont College.

Learning how to use a certain platform to present their information was another problem they had to face. The team of three worked many weeks learning two different things that would bring everything together.

“I learned a lot about LaTeX in the process of preparing my research for a presentation. Using LaTeX is fantastic, but it’s challenging at first,” said Bowen.

After learning two new things, Rebecca and Julia were ready to present their work. However, all the research they found couldn’t be presented at the Symposium, because they got way more information than intended.

“Coming up with the proof took longer than I would’ve imagined. I was hoping to prove several results, but research is a lot different from regular classwork,” said Graham.

The amount of research that Bowen and Graham had to find would have anyone’s brain burnt out, but with the help of Dr. Torrance, they felt like they conquered the world. Even though this math challenge is complete, they are excited to increase her knowledge even more.

“I was thrilled with the whole research process, and I’m looking forward to continuing to think about Trangles and exploring other new topics in mathematics in the future,” said Bowen.

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