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The College Mathematics Journal

Volume 49, 2018 - Issue 5
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Articles

Archimedes Redux: Center of Mass Applications from The Method

Shirley GrayView further author information
&
Cye H. WaldmanView further author information
Pages 346-352
Published online: 16 Nov 2018
 
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Acknowledgments

We are deeply grateful for the expert assistance of Sam Chyau, who verified all the equations and typeset the manuscript.

Summary

Archimedes showed that a particular hoof, defined in terms of a triangular prism and a half cylinder, has area 1/6 of a bounding cube. Motivated by recent commentary on Archimedes’s work, we find the centers of mass for the hoof, prism, and half-cylinder and find, for instance, that they are collinear. We also posit that Archimedes could have made the same observations with the mathematical tools available to him.

Additional information

Notes on contributors

Shirley Gray

Shirley Gray (, MR ID 635930) received her Ph.D. from the University of Southern California, and is a professor emerita of the California State University, Los Angeles. She was awarded the 2016 MAA Distinguished Teaching Award of the Southern California–Nevada Section of the MAA. In recent years, Gray and Waldman have collaborated on applying modern mathematics to various Archimedean methods and proof. Their eureka moment came when they discovered the golden ratio hidden in one of Archimedes’s propositions.

Cye H. Waldman

Cye Waldman (, MR ID 774855) received a Ph.D. from Princeton University and is now retired after a fifty-year career in mathematical modeling. He has developed new paradigms and techniques in plane curves, tessellations, and fractals. Waldman’s design for a Pi Day T-shirt has been spotted at the Museum of Mathematics in New York City and recent Joint Mathematics Meetings.

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