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Mathematics major Jordan Tirrell ’08 (West Grove, Pa.)is studying integers and 90-degree angles with Cliff Reiter, professor of mathematics. More specifically, he is learning about the perfect cuboid problem, an open mathematical problem about 3-D boxes.
“We are studying the variant where angles other than 90 degrees are allowed [in a perfect cuboid],” Reiter explains.
The notion behind the research is that every edge in the 3-D box – created by seven lengths and diagonals – is an integer. The researchers are working to find the first perfect cuboid.
“The perfect cuboid problem has been an open question for a long time and nobody has been able to find one or prove that they don’t exist,” says Tirrell.
Reiter says that Tirrell is a bright student who asks insightful questions, develops mathematical examples, and assists in finding relevant literature on the topic.
The collaboration is part of Lafayette’s distinctive EXCEL Scholars program, in which students conduct research with faculty while earning a stipend. The program has helped to make Lafayette a national leader in undergraduate research. Many of the more than 160 students who participate each year share their work through articles in academic journals and/or conference presentations.
As his mentor, Reiter is helping Tirrell develop his skills in writing papers, presenting mathematical data, and completing computer calculations. His role in the collaboration is to locate theorem statements and proofs about the perfect cuboid problem.
“Discussing math culture is fun and valuable in the math context where Jordan is experiencing it,” Reiter says. “[This research] will also carry over to his work on projects in other courses or in the work environment.”
Tirrell and Reiter are using a parallelpiped, or a slanted box made of six parallelograms. If the results are promising, they may be published in a scholarly journal, Tirrell says.
For a majority of the summer, Tirrell worked on gathering theorems and testing their proofs. Although he continues to do research on perfect cuboids, the majority of his time on the EXCEL project is now spent writing a paper and tying up the loose ends of the existing research.
“Even though we have not found a perfect parallelpiped, we have been able to come close,” he says. “The things we have discovered along the way are really of interest.”
According to Reiter, Lafayette’s environment is conducive to the level of academic research in the EXCEL program.
“There are great opportunities for working closely with faculty in upper-level courses and on undergraduate research experiences,” he says.
In the past seven years, Reiter has mentored over 30 students in various academic projects, including work with Prince Chidyagwai ’05 (Marondera, Zimbabwe), a double major in mathematics and computer science, on the mathematical generation of snowflake patterns. The project was featured as the lead story on Nature magazine’s web site and also will appear in Chaos, Solutions and Fractals.
As a result of the research project and his experience at Lafayette, Tirrell says that he eventually wants to teach at a college or university.
He is a member of the tennis and table tennis clubs and works in the math department.
As a national leader in undergraduate research, Lafayette sends one of the largest contingents to the National Conference on Undergraduate Research each year. Thirty-nine students were accepted to present their research at this year’s conference.