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Reflections on the Arbelos

Year of Award: 2007

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 113, (2006), pp. 236-249

Summary: (from the author's abstract) The geometric shape bounded by three mutually tangent semi-circles having collinear diameters was named the arbelos by Archimedes. The arbelos has many surprising geometric properties, some known to the ancient Greeks and some discovered in modern times. The geometry of reflections offers insight on the arbelos, but a full appreciation of its properties, like the work of Archimedes, reflects other subjects too, such as number theory and mechanics.

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About the Author: (from Prizes and Awards, Joint Mathematics Meetings 2009) Harold P. Boas, the son of a physicist and of a mathematician, received degrees in 1976 and in 1980 from universities on the Charles River in Cambridge, Massachusetts. Since 1984, he has taught mathematics to Texas Aggies. Jointly with Emil J. Straube, he received the 1995 Stefan Bergman prize for research in multidimensional complex analysis. A former editor of the Notices of the American Mathematical Society (2001– 2003) and of the book review column in this MONTHLY (1998–1999), he believes that effective communication of mathematics is a learnable skill.

 

Author (old format): 
Harold P. Boas
Author(s): 
Harold P. Boas
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Publication Date: 
Wednesday, October 22, 2008
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Summary: 
The geometric shape bounded by three mutually tangent semi-circles having collinear diameters was named the arbelos by Archimedes. The arbelos has many surprising geometric properties, some known to the ancient Greeks and some discovered in modern times. The geometry of reflections offers insight on the arbelos, but a full appreciation of its properties, like the work of Archimedes, reflects other subjects too, such as number theory and mechanics.

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