You are here

The Circle-Square Problem Decomposed

Year of Award: 2010

Award: Trevor Evans

Publication Information: Math Horizons, Nov. 2009, pp. 19-21, 31

Summary: This article examines Miklós Laczkovich's 1990 result 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. Enabling readers to gain visual understanding of Laczkovich's theoretical result, the article studies how closely the circle-squaring process can be approximated using polygons that can be moved only with translation.

Read the Article

About the Authors

Pamela Pierce is a professor of mathematics at The College of Wooster, in Wooster, Ohio. She holds a B.A. from Amherst College, an M.Ed. from the University of Massachusetts, and a Ph.D. in Mathematics from Syracuse University. Her primary area of research is real analysis, focusing on functions of generalized bounded variation. This year she received an NSF grant to help fund the 34th Summer Symposium in Real Analysis, which she hosted at Wooster last month. In recent years she has been active in leading undergraduate research projects as part of the summer AMRE program at Wooster. In 2008 she hosted the Midstates Conference for Undergraduate Research in Computer Science and Mathematics. In 2009 her team of student researchers was selected to participate in the CUR-sponsored Posters on the Hill– session in Washington, D.C. Pam enjoys teaching the talented students at Wooster, in courses such as calculus and real analysis. Recently she served a two-year term as an associate dean at Wooster. She is currently serving as the department chair. Pam was a fellow in Project NExT (a blue dot) and is a consultant for the current class of NExTers.

John Ramsay is a professor of mathematics at The College of Wooster. He holds a B.A. from Berea College and an M.S. and Ph.D. from the University of Wisconsin, Madison. His doctoral work was in algebraic topology and he completed a Ph.D. minor in operations research. He is just completing a sabbatical leave and is looking forward to getting back into the classroom where he has enjoyed teaching Wooster students for the past 23 years. John is founder and director of Wooster‘s 17-year old AMRE program. AMRE is a summer consulting and research 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. Most recently John has worked with a team on a consulting project for Goodyear Tire and Rubber and on a research team working in knot theory.

Hannah Roberts is a junior mathematics major at The College of Wooster, and is from Youngstown, Ohio. Hannah and Nancy Tinoza worked on the circle squaring problem in the summer of 2009. They made improvements to the dissection algorithm that reduced the number of pieces needed in the dissections.

Nancy Tinoza is a junior mathematics and economics double major at The College of Wooster. She is from Harare, Zimbabwe.

Jeff Willert is a 2009 graduate of The College of Wooster, and is from Chagrin Falls, Ohio. He is currently in his second year of a Ph.D. program in mathematics at North Carolina State University. Jeff worked on the circle squaring problem in the summers of 2007 and 2008. He and Wenyuan Wu developed the initial dissection algorithm.

Wenyuan Wu is a senior mathematics and economics major at The College of Wooster. She is from Chengdu, China. Wenyuan worked on the circle squaring problem in the summer of 2008.

MSC Codes: 
97G40, 97E60
Author(s): 
Pamela Pierce (College of Wooster), John Ramsay (College of Wooster), Hannah Roberts (College of Wooster), Nancy Tinoza (College of Wooster), Jeffrey Willert (North Carolina State University), and Wenyuan Wu (College of Wooster)
Flag for Digital Object Identifier: 
Publication Date: 
Thursday, August 19, 2010
Publish Page: 
Summary: 

This article examines Miklós Laczkovich's 1990 result 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. Enabling readers to gain visual understanding of Laczkovich's theoretical result, the article studies how closely the circle-squaring process can be approximated using polygons that can be moved only with translation.