Wooster Mathematicians Shed New Light on Tarski's Circle-Squaring Problem
Wooster Mathematicians Shed New Light on Tarski's Circle-Squaring Problem
Professors Pam Pierce and John Ramsay, along with four students, receive Trevor Evans Award
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Hannah Roberts, John Ramsay, Pam Pierce, and Wenyuan Wu accept the Trevor Evans Award at the Mathematical Association of America Conference.
WOOSTER, Ohio - At last, mathematicians have figured out how to fit a square peg into a round hole. Well, not exactly. What they have done is determine how to illustrate the decomposition of a circle and reassemble it to fit into the same area as a square. "The best way to illustrate the problem was to approximate the circle by a many-sided regular polygon and then develop an algorithm that can reconfigure the polygon into a square," said Pam Pierce, professor of mathematics and computer science at The College of Wooster and the lead researcher on the project. "To the naked eye, the transformation of a 40-gon into a square looks very much like a circle-to-square decomposition.
Pierce was joined by John Ramsay, also a professor of mathematics and computer science at Wooster, and four students - Hannah Roberts, Nancy Tinoza, Jeffrey Willert, and Wenyuan Wu. The six mathematicians received the Trevor Evans Award for their article, "The Circle-Square Problem Decomposed," which appeared in the November 2009 edition of Math Horizons.
The award-winning article examines Miklós Laczkovich's famous 1990 finding that a circle can be decomposed into a square of the same area, which is a task not attainable with paper and scissors (as proven by Dubins, Hirsch and Karush in 1964). By providing a visual understanding of Laczkovich's theoretical result, the article explains how closely the circle-squaring process can be approximated using polygons that can be moved only with translation. By the end of the article, the reader will understand how to dissect an n-gon to form a square and why a method of dissection answers the challenge of decomposition. The article also offers suggestions for the number of pieces necessary for such constructions.
"It's an honor to be recognized for an article that was selected as one of the two best in Math Horizons during the past year," said Pierce. "The award was based on the clarity of the article and value of its content. It's also unique in that several undergraduates contributed to the research. Most articles in this publication do not include work with undergraduates. This speaks highly of the quality of research conducted by the students at Wooster."
Pierce, who holds a B.A. from Amherst College, an M.Ed. from the University of Massachusetts, and a Ph.D. in mathematics from Syracuse University, specializes in the area of real analysis, with a focus on functions of generalized bounded variation. Ramsay, who holds a B.A. from Berea College and an M.S. and Ph.D. from the University of Wisconsin, Madison, specializes in algebraic topology. He is the founder and director of Wooster's Applied Mathematics Research Experience (AMRE), a summer program that employs Wooster students and faculty in consulting projects for business and industry in northeast Ohio as well as in mathematics and computer science research projects.
Roberts, a junior mathematics major at Wooster and a resident of Youngstown, and Tinoza, a junior mathematics and economics double major and a resident of Zimbabwe, worked together on the circle-squaring problem last summer, when they made improvements to the dissection algorithm that reduced the number of pieces needed in the dissections.
Willert, a 2009 Wooster graduate and a resident of Chagrin Falls, Ohio, who is now in his second year of a Ph.D. program in mathematics at North Carolina State University, and Wu, a senior mathematics and economics major and a resident of Chengdu, China, did much of the initial work on the approximate circle-squaring algorithm during the summers of 2007 and 2008.
The Trevor Evans Award was established by the Board of Governors in 1992 and first awarded in 1996 to honor the distinguished mathematician, teacher, and writer from Emory University.