The Method of Exhaustion

The Method of Exhaustion is a mathematical technique used to find the area of shapes by breaking them down into smaller, manageable parts. Imagine trying to measure the area of a circle by inscribing it with polygons (like triangles or squares) whose areas you can calculate easily. By increasing the number of sides of these polygons, their total area gets closer to the area of the circle. This method, developed by ancient mathematicians like Archimedes, effectively "exhausts" the possibility of finding the area by converging on the exact value through limiting processes.