Student Researchers: Nancy TInoza and Hannah Roberts
Faculty Advisor: Pamela Pierce (Mathematics)
In 1925 Alfred Tarski asked whether it was possible to decompose a circle into a finite number of pieces and rearrange these pieces to form a circle. While this cannot be physically accomplished with paper and scissors, in 1990 Laczkovich proved that this was theoretically possible and put the upper bound on the number of pieces as 1050.
In the summers of 2007 and 2008, the Mathematics Department received a grant from the Howard Hughes Medical Institute to work on this Tarski's Circle Squaring Problem. During that time, students worked to develop a visual approximation of the circle squaring process, and they developed an algorithm for counting the number of pieces.
During the summer of 2009, Nancy Tinoza '12 and Hannah Roberts '12 continued this research. First, they made improvements to the way that the polygons were dissected. The overall process remained the same, but some of the specifics, such as the orientation of the original polygon, were altered. This enabled the development of a single equation for counting the number of pieces in an n-gon. As a result, they had a monotone graph.
However, their most important project was to find an upper bound for the number of pieces. Through looking for this upper bound, they also found an interesting connection between the sum of divisors and the number of boxes, a specific type of piece within the dissection process.
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Areas of Study
Taylor Hall308 E. University StreetWooster, OH 44691Phone: 330-263-2478JMiddleton@Wooster.edu
1189 Beall Avenue, Wooster, Ohio 44691. (330) 263-2000
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