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Reflections on the Arbelos

Award: Chauvenet Prize

Year of Award: 2009

Publication Information: American Mathematical Monthly, 113 (2006), no. 3, 236–249.

Summary: An arbelos is the region bounded by three semicircles, tangent in pairs, with diameters on the same line. The author includes the surprising discovery that the linear algebra theorem tied to Mohr’s circle, which comes up in analyzing shear stress in solid mechanics, is an arbelos.

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About the Author: (From Prizes and Awards, Joint Mathematics Meetings 2009) Harold P. Boas is professor of mathematics at Texas A&M University in College Station. His cited article on the arbelos, which also received the 2007 Lester R. Ford Award from the MAA, is a departure from his primary research interest in multi-dimensional complex analysis. He shared the 1995 Stefan Bergman Prize with his collaborator Emil J. Straube for progress on the boundary-regu­larity theory of solutions of the inhomogeneous Cauchy–Riemann equations on pseudoconvex domains. He has served as book-review editor of the American Mathematical Monthly (1998–1999), as editor of the Notices of the American Math­ematical Society (2001–2003), and as editor of the Anneli Lax New Mathematical Library (2007–2009). He has supervised the dissertations of four Ph.D. students.

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Harold P. Boas
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Harold P. Boas
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Publication Date: 
Wednesday, August 26, 2009
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An arbelos is the region bounded by three semicircles, tangent in pairs, with diameters on the same line. The author includes the surprising discovery that the linear algebra tied to Mohr's circle, which comes up in analyzing shear stress in solid mechanics, is an arbelos.

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