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Aquinas Math Professor Publishes Textbook

“Geometry by Construction” includes the undergraduate research work of five AQ students.

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McDaniel with textbook

GRAND RAPIDS, Mich. – The undergraduate research work of five Aquinas College students have resulted in the development of their own geometry theorems. Aquinas math professor Mike McDaniel, Ph.D. will be highlighting their work in his newly released geometry textbook, “Geometry by Construction.”

The student researchers include: Noah Davis ‘15, who analyzed squaring the circle in the hyperbolic disk; Jillian Duffey (Russo) ‘10, who worked on the hyperbolic polygonal spirals; Nathan Poirier ‘11, who researched Alhazen’s hyperbolic billiard problem; and Kyle Jansens ‘15 and Noah Davis, who worked together on a do-it-yourself problem for squaring the circle.

Though all were working on unique projects, Davis, Duffey (Russo), Poirier and Jansens assisted in the creation and verification of new geometrical ideas and provided constructions for important geometric objects. All of their theorems have been reviewed by math professors, verified as both new and true, were individually published in the Rose-Hulman Undergraduate Math Journal, and have now been re-published in “Geometry by Construction.”

"Including undergraduate research as theorems is extremely unusual for any textbook because these theorems have to be verified,” said McDaniel. “Luckily, four of my five researchers have their work in refereed journals - their theorems are solid.”

“Geometry by Construction” was released in February 2015. Aquinas College’s mathematics department promotes the study of mathematics in depth in preparation for graduate school or an immediate career, supports the mathematical needs of other disciplines and supplies a curriculum for all students to enhance their understanding of mathematical thought.