PatternsOfThinking

 

  The method of exhaustion is a mathematical technique developed by ancient Greek mathematicians like Eudoxus and Archimedes. It was a precursor to modern calculus, used to determine the area or volume of a shape by inscribing and circumscribing polygons or polyhedra within it. How Does it Work? Inscribe and Circumscribe: A sequence of polygons or polyhedra is inscribed within the shape, and another sequence is circumscribed around it. Approximation: As the number of sides or faces of these shapes increases, their areas or volumes converge towards the area or volume of the original shape. Exhaustion: The "exhaustion" comes from the idea that the difference between the inscribed and circumscribed shapes becomes increasingly small, "exhausting" the space between them. Proof by Contradiction: Mathematicians often used a proof by contradiction to demonstrate that the area or volume of the original shape must lie between the limits of the inscribed and circumscr...