Definition:Method of Exhaustion

Definition
The method of exhaustion is a technique for calculating an approximation to the physical extent of a geometric figure whose extremities are curved lines.

To measure the area of a circle, for example, this is done by:
 * Circumscribing a polygon around the circle
 * Inscribing a polygon inside the circle
 * Measuring the areas of those polygons
 * Noting that the area of the circle is between those two
 * Increasing the number of sides on those polygons to make them closer and closer to the circle and each other.

As the number of sides of the polygons increases, their areas become ever closer to each other.

Historical Note
The method of exhaustion was invented by in around 370 BCE.

It was later exploited to good effect by, and is used throughout during the course of calculating volumes of solid figures.