Exhausting Circles: The Greek Path to Calculus

A deep dive into the method of exhaustion, the ancient Greek technique of finding areas and volumes by squeezing shapes with inscribed and circumscribed polygons. We trace its origins with Antiphon and Bryson, see how Eudoxus formalized it through the theory of proportion, and follow the line from these ideas to modern calculus—through limits, convergence, and rigorous reductio arguments.

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