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A Postmodern View of Fractions and the Reciprocals of Fermat Primes
Award: Carl B. Allendoerfer
Year of Award: 2001
Publication Information: Mathematics Magazine, Vol. 73(2000), pp. 83-97
Summary: Applying the techniques of fractal geometry to visualizing fractions.
About the Authors: (from Mathematics Magazine, Vol. 73 (2000)) Rafe Jones received a bachelor's degree in mathematics and French from Amherst College in 1998. He received his Ph.D. from Brown University and is a visiting professor at University of Wisconsin-Madison. His involvement in the world of fractions stems from an informal summer research project with Prof. Pearce. Throughout the lengthy project, he has examined the graphs of hundreds of fractions, and delighted in discovering the often unexpected personality of each image.
Jan Pearce has been teaching mathematics and computer science at Berea College since 1992. She received her Ph.D. in mathematics from the University of Rochester, and her B.A. from Augustana College in Rock Island, Illinois, with majors in computer science, mathematics, and physics. Her research interests range widely, from environmental modeling research to number theoretic work like that explored in the present article. She enjoys involving students in research -- which is, in fact, how this article came into being. She and Rafe Jones began these explorations while Rafe Jones was a high school student taking mathematics courses at Berea College. During the scant hours in which she is not working, Jan Pearce enjoys participating in traditional music and dance.