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Modernizing Archimedes’ Construction of π

Author

Listed:
  • David Weisbart

    (Department of Mathematics, University of California, Riverside, CA 92521, USA)

Abstract

In his famous work, “Measurement of a Circle,” Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern approaches for defining π eschew his method and instead use arguments that are easier to justify, but they involve ideas that are not elementary. This paper makes Archimedes’ measurement procedure rigorous from a modern perspective. In so doing, it brings a rigorous and geometric treatment of the differential properties of the trigonometric functions into the purview of an introductory calculus course.

Suggested Citation

  • David Weisbart, 2020. "Modernizing Archimedes’ Construction of π," Mathematics, MDPI, vol. 8(12), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2204-:d:460574
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