During the spring 2011 semester, AQ senior and double major in mathematics and physics, Nate Poirier, attended the annual Rose-Hulman Institute of Technology Undergraduate Mathematics Conference to present his essay entitled “Alhazen’s Billiard Problem in Hyperbolic Geometry.”

The complex project began in the summer of 2010 and concluded the subsequent fall when it was submitted for revision in Berkeley’s math journal, Involve. The three months of research were funded by the Aquinas Thompson-Mohler Summer Research Scholarship, which provides assistance to AQ students embarking on a science project with the guidance of a faculty member. During the Indiana conference on March 25 and 26, Poirier attended multiple student and faculty presentations as well as demonstrated his theory regarding a possible solution to an age-old problem.

Though Poirier’s current ambitions include the research and presentation of mathematical theories, he originally chose Aquinas for its athletic possibilities. “Running was what sold me on going here,” said Poirier, member of both the men’s track and cross country teams for the past five years. A Warren, Mich. native, he learned of the College teams through a fellow runner.

His academic interests began in the history and philosophy departments until he completed an astronomy class during his first semester. “I had an interest in many things,” said Poirier who, after realizing his passion for science, declared his mathematics major during his freshman year. He then added a contract major in physics as a sophomore.

In the spring of 2010, Poirier was approached by Aquinas Math Professor Michael McDaniel, Ph.D., who suggested the student-professor collaboration on the over 2000 year old theory. “I kind of jumped at the opportunity,” said Poirier.

The abstract for the essay reads as follows: “Alhazen’s billiard problem gives points A and B inside a circle and seeks an inscribed isosceles triangle with a given point on each leg. In our summer research, we found a bijection between Euclidean solutions and hyperbolic solutions. The constructible Euclidean cases pair up with the constructible hyperbolic cases.”

In essence, Poirier and McDaniel proved the impossibility of a theory from Euclidean geometry in terms of an entirely different math language. “Another new theorem is thus added to mathematics,” said McDaniel.

In reaction to his presentation experience, Poirier said, “Hopefully I will be doing it a lot more in the future.” Encouraged by the opportunity to share his research, Poirier continues to search for additional mathematics conferences within Michigan. At the Rose-Hulman event, he also had the opportunity to witness the accomplishments of fellow students, and was amazed at the mathematical progress and determination of his peers. “It was, I guess, inspirational,” Poirier said. “It was really cool to see what other kids could do.”

This fall, he will begin a mathematics doctorate program at Western Michigan University and considers a career in teaching for the possibility to “inspire and encourage the next generation.”