Method of exhaustion

Definition

The method of exhaustion is an ancient mathematical technique used to find the area under a curve by inscribing and circumscribing polygons. It involves calculating the areas of these polygons and taking the limit as the number of sides increases indefinitely.

5 Must Know Facts For Your Next Test

1. The method of exhaustion is considered a precursor to integral calculus.
2. It was developed by ancient Greek mathematicians, including Eudoxus and later used by Archimedes.
3. This method relies on the concept of limits to approximate areas more accurately as the number of polygon sides increases.
4. It can be visualized as filling an area with increasingly smaller sections that more closely fit the shape being measured.
5. The precision of this method improves as the number of subdivisions or polygons increases.

Review Questions

Related terms

Integral: A fundamental concept in calculus that represents the area under a curve. It can be interpreted as an accumulation function.

Limit:

A value that a function approaches as the input approaches some value. Limits are essential for defining integrals and derivatives.

Riemann Sum: An approximation of an integral by summing up areas of rectangles (or other shapes) under a curve. It serves as a modern counterpart to methods like exhaustion.