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Figures Circumscribing Circles

by Tom Apostol and Mamikon Mnatsakanian

Year of Award: 2005

Publication Information: The American Mathematical Monthly, vol. 111, no. 10, December 2004, pp. 853-863.

Summary: The centroid of the boundary of an arbitrary triangle need not be at the same point as the centroid of its interior, but the two centroids are always collinear with the center of the inscribed circle, at distances in the ratio 3 : 2 from the center. This paper generalizes this elegant and surprising result to any polygon that circumscribes a circle.

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About the Authors: [from The American Mathematical Monthly, v. 111, no. 10, (2004)]

Tom Apostol joined the Caltech mathematics faculty in 1950 and became professor emeritus in 1992. He is director of Project MATHEMATICS! ( an award-winning series of videos he initiated in 1987. His long career in mathematics is described in the September 1997 issue of The College Mathematics Journal. He is currently working with colleague Mamikon Mnatsakanian to produce materials demonstrating Mamikon’s innovative and exciting approach to mathematics.

Mamikon Mnatsakanian received a Ph.D. in physics in 1969 from Yerevan University, where he became professor of astrophysics. As an undergraduate he began developing innovative geometric methods for solving many calculus problems by a dynamic and visual approach that makes no use of formulas. He is currently working with Tom Apostol under the auspices of Project MATHEMATICS! to present his methods in a multimedia format.


Subject classification(s): Geometry and Topology
Publication Date: 
Tuesday, September 23, 2008