Year of Award: 2005

Publication Information: The American Mathematical Monthly, vol. 111, no. 6, June/July 2004, pp. 496-508.

Summary: Among Archimedes' great discoveries is the fact that the volume of a solid sphere is two-thirds the volume of the smallest cylinder that surrounds it, and that the surface area of the sphere is also two-thirds the total surface area of the same cylinder.  This paper generalizes Archimedes' method to derive other interesting results about area and volume.

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About the Author(s): (from The American Mathematical Monthly, v. 111, (2004)) Tom Apostol joined the Caltech mathematics faculty in 1950 and became professor emeritus in 1992. He is director of Project MATHEMATICS! (http://www.projectmathematics.com) 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.