The Euclidean Discus Toss

Abstract

The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to toss and catch frisbees in a collaborative and hands-on effort designed to sharpen modular arithmetic skills, enhance familiarity with iterative and recursive algorithms, and strengthen classroom community. The activity is fun, low-stakes, and can be customized to meet a variety of pedagogical objectives.

Keywords:

• Active learning
• tactile learning
• extended Euclidean algorithm
• Euclid's algorithm
• Bézout's identity
• recursive programming
• greatest common divisor
• modular arithmetic

ACKNOWLEDGMENTS

The authors would like to thank our former students, Madison, Andy, and Edward, for the use of their action photos in our paper. The authors are also grateful to the editor and the referees for their useful comments and suggestions that improved this manuscript.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Matthew A. Morena

Matt Morena studied chaotic and nonlinear dynamical systems while earning his Ph.D. from the Integrated and Applied Mathematics program at the University of New Hampshire. He is currently an assistant professor of mathematics at Christopher Newport University, having previously taught at Young Harris College. In addition to mathematics, he also enjoys hiking, gardening, traveling, and perfecting his Hammer Throw.

Michael D. Smith

Mike Smith has taught all levels of mathematics at Lycoming College in Williamsport, PA for the past eleven years. He is an unflinching non-conformist, known for his Fun Friday activities and his belief that classes should push students out of their comfort zones. He grew up in Maine and earned his Ph.D. in non-associative algebra from the University of Virginia in 2006.