# Harvey Plotter and the Circle of Irrationality

by Nathan Carter (Bentley University) and Dan Kalman (American University)

Year of Award: 2012

Award: Trevor Evans

Publication Information: Math Horizons, Nov. 2011, pp. 10-13

Summary: The evil Lord Voldemorphism is trying to find the rational points on the unit circle. Harvey Plotter and his faithful companions, Hymernie and Rong, must try to determine the rational points before Lord Voldemorphism. Rong mentions that a line between two rational points always has a rational slope. He suggests they begin with (0, -1) and draw a line with rational slope; then the other point will be rational. Hymernie knows Rong is confusing the converse with the contrapositive. With some work they prove Rong's conjecture. They begin finding one rational point at a time, but they need all the rational points. A friendly suggestion by Professor Alphas Jumblemore reminds them to use a general p/q for the rational slope. Once done they realize that the rational points are Pythagorean Triples.

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About the Authors

Nathan Carter uses computer science to advance mathematics. He studied both subjects at the University of Scranton and at Indiana University, earning a Ph.D. in mathematical logic in 2004. He then joined the faculty of Bentley University and has worked in logic, written the book Visual Group Theory, and dabbled in social network analysis. He writes open source mathematics software, including Group Explorer for group theory visualization, and Lurch, a general validation environment for mathematical reasoning.

Dan Kalman has been a member of the mathematics faculty at American University, Washington, D.C., since 1993. Prior to that he worked for eight years in the aerospace industry and taught at the University of Wisconsin, Green Bay. Kalman has a B.S. from Harvey Mudd College and a Ph.D. from University of Wisconsin, Madison. He has been a frequent contributor to all of the MAA journals, has published two books with the MAA, and has served on the editorial boards of both MAA book series and journals. Kalman has served the national and regional MAA in several capacities, including a term as associate executive director for programs, as the current governor for the MD-DC-VA section, and as a cast member of both productions of "MAA: The Musical!"

Subject classification(s): Numbers and Computation | Number Concepts | Rational Numbers | Geometry and Topology | Plane Geometry | Triangles
Publication Date:
Tuesday, August 7, 2012