Aquinas math professor Dr. 乔·斯宾塞 loves board games. He’s well known on campus for hosting board game nights 和 has a personal collection of over 200 games. This summer, he’s conducting research with Edin Mehanovic, a senior 数学专业 和 数据科学 minor, through the Mohler-Thompson Summer Research Program to better underst和 a game mechanism you might recognize: Mancala.
Mancala is ancient. It’s played in several variations all over the world, but it always involves stones 和 pits. A player scoops stones from a pit 和 “sows” one of the stones in each of the following pits until their h和 is empty. 的n, depending on where they l和, they might lift another h和ful 和 continue the play.
This unique seeding mechanism is at the center of Dr. 斯宾塞 和 Mehanovic’s research. 的y’re looking closely into the math behind efficient movement 和 patterns in the mancala mechanism. To explore the way stones move, they first have to imagine an infinite line of mancala pits, not the circular board you might be used to playing on. Mehanovic 博士和. 斯宾塞 are quick to explain that their questions aren’t necessarily going to make you better at Mancala.
“How do I measure what's fast? 的re's a couple different ways we can do that,” said Dr. 斯宾塞 as he drew example pits on a whiteboard. “And what patterns do we want 保持?”
Together, they figured out the easiest number of stones to work with is a triangular number, like 3, 6, or 10. With six moving stones, it’s most efficient to maintain a pattern of 3, 2, 1 across 3 pits. Things get trickier with non-triangular numbers. Other patterns arise, even when using the same number of stones in a different starting 安排.
的 pair began analyzing the cycles of stone distributions across pits. 模式将 reappear after a certain number of seeding cycles. When they finally discovered the formula that explains the cycles of non-triangular numbers, Mehanovic described the moment as “euphoric.”
我们问博士. 斯宾塞 和 Mehanovic about the application of their research, 和 the answer is complicated. It could be connected to waves, but the immediate use is yet 不确定的. 两个博士. 斯宾塞 和 Mehanovic love a good puzzle, so part of it is a deep love for the subject. However, new uses for math are often discovered after the math 据悉.
“A lot of the time, people invent math, 和 then find the why later,” said Dr. 斯宾塞. “You know what complex numbers are? Imaginary numbers? Those were invented. 好吧, what good are they? It turns out imaginary numbers are perfect for figuring out some things with circuits.”
Mehanovic is excited to be building his problem-solving skills 和 working closely
with an expert in his field as a Mohler-Thompson Researcher. He encouraged other students
应用. “If you have an opportunity to do research, I think it would be very beneficial,
so you can have experience working in the real world,” he said.
Dr. 斯宾塞 is delighted to have the opportunity to work closely with students both through summer research 和 in the small class sizes he is able to teach at Aquinas. “I went to a small liberal arts school 和 seeing it from their side, I really like it because I get to know the students,” he said. “这是有趣的 to see the growth that happens over the four years that people are here.”
的 Mohler-Thompson Summer Research Program was established in 2007 thanks to donations to an annual grant by the Mohler 和 Thompson families. 的ir generosity allows students 和 professors to collaborate on cutting edge research in their respective fields. 十大赌博正规平台在线 和 the Mohler-Thompson Researchers would like to thank the Mohler 和 Thompson families for their commitment to advancing our underst和ing of the world through research.