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The AMATYC Review Spring 2006, Vol.27, No.2 |
The Radical Axis: A Motion
Study |
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Ray McGivney is Professor of Mathematics at the University of Hartford. He earned his AB and MA in mathematics at Clark University and his PhD in mathematics at Lehigh University. He has served as mathematics consultant for several school systems in Connecticut and presented at numerous local, regional and national professional meetings. E-mail: mcgivney@hartford.edu |
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James McKim, now at Winthrop University, holds a PhD in mathematics from the University of Iowa. He has taught mathematics and computer science for more than 30 years, the last 15 mainly to working professionals. He is the coauthor (with Ray McGivney and Ben Pollina) of two mathematics textbooks and the author of several articles in both computer science and mathematics. E-mail: mckimj@winthrop.edu |
| Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still exists. We are interested in the relationship of this line to the two circles in this latter case. We take an algebraic approach to its formula so we can see this relationship as we move and scale the defining circles. This approach culminates in the discovery that if the two circles grow so that their areas increase at equal rates then the radical axis remains constant and in fact is the eventual line of intersection of the two circles. | |
