Mathematics at Aquinas College

Research

Dr. Mike McDaniel has written a book, Geometry by Construction: Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries, which uses results of his many successful undergraduate research projects at Aquinas.  Read more.

Current student research

  • Aimee Judd investigated the combinatorics of citation networks in 2018-19.  Aimee presented her work at the West Michigan Regional Undergraduate Science Research Conference at the Van Andel Research Institute in November, where she was one of only four undergraduate students chosen to give a talk at the conference, and she also presented a poster of her research at the MAA meeting at the University of Detroit-Mercy in April.
  • Kelsey Hall did research in non-Euclidean geometry, proving new theorems about pedal triangles.  Kelsey presented a poster at the West Michigan Regional Undergraduate Science Research Conference at the Van Andel Research Institute in November, and she contributed a talk on her work at the Rose-Hulman Undergraduate Math Conference in April.   Kelsey and Dr. McDaniel have submitted a paper for publication which is currently under review.

Other recent student research:

  • 2017-18
    • Holly Ensley and Dr. Spencer continued work from the previous year, studying mathematical problems arising from the game Mancala.
    • Paul Gass and Dr. McDaniel extended results from Euclidean geometry to hyperbolic geometry.
  • 2016-17
    • Maria Maguire and Dr. Spencer initiated a study of certain mathematical problems arising in the game Mancala.
    • Tristen Spencer and Dr. McDaniel completed a project, “Euclidean measurements for hyperbolic constructions”.  They have submitted a paper for publication which is currently under review.  
  • 2015-16
    • Jacob Campbell and Dr. Fox researched properties of circulant graphs, including their independence numbers.
    • Cecilia Magnuson and Dr. McCarty researched higher order thinking in middle school mathematics classrooms.
  • 2014-15
    • Krystin Dreyer and Dr. Fox studied the mathematics of citation networks.
    • Kyle Jansens and Dr. McDaniel completed the long story of squaring the circle.  It’s been known since 1882 that in Euclidean geometry, it’s impossible to construct, using only a straightedge and compass, a square with the same area as a given circle.  In 2012, Noah Davis and Dr. McDaniel proved that such a construction is possible in hyperbolic geometry, and Kyle and Dr. McDaniel proved it’s also possible in elliptic geometry.  Their result was published in the Rose-Hulman Undergraduate Math Journal, and Kyle, co-author Noah Davis, and Dr. McDaniel even made the local news!  Read Kyle’s and Noah’s paper here.
  • 2013-14
    • Noah Armstrong and Dr. Spencer studied the mathematics of the game Mancala.
    • Noah Davis and Dr. McDaniel proved that it’s possible to square the circle in hyperbolic geometry.  Noah presented his results at MathFest in Portland, Oregon, and his paper was published in Rose-Hulman Undergraduate Math Journal.  Read Noah’s paper here.
  • 2012-13
    • Jackie Gipe and Dr. McDaniel worked on a project titled, “Invertible Chord Diagrams from the Wheel.”  Jackie presented her work at a Calvin College colloquium.
  • In addition to the publications mentioned above, AQ math student publications include:
    • “Tangent circles in the hyperbolic disk”, by Megan Ternes.  Appeared in Rose-Hulman Undergraduate Math Journal, 2013.  Read it here.
    • “Fibonacci numbers and chord diagrams”, by Jane Kraemer.  Appeared in Pi Mu Epsilon Journal, Spring 2011, Vol. 13, No. 4.  Read it here.
    • “Hyperbolic polygonal spirals”, by Jillian (Russo) Duffy.  Appeared in Rose-Hulman Undergraduate Math Journal, Fall 2010 Vol.  Read it here.
    • “Alhazen’s hyperbolic billiard problem”, by Nate Poirier.  Appeared in Involve, Vol. 5, No. 3, 2012.  Read it here.

“I loved the opportunity to take the skills that I have learned in my math classes and combine them with some creativity, to make something new and exciting for the math world. It was a challenge that I truly enjoyed!”
Aimee Judd
Class of 2020