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arXiv · 2009.06752

Modernizing Archimedes' Construction of $\pi$

David Weisbart
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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 $\pi$ 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.

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David Weisbart. 2020-09-14. Modernizing Archimedes' Construction of $\pi$. https://arxiv.org/abs/2009.06752

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