Exhaustion method

This article explains the method of exhaustion in mathematics; for exhaustive algorithms, see the brute force method .

The exhaustion method is an ancient method for calculating areas, i.e. for integration .

Antiphon (430 BC) was convinced that you should be able to square a circle , since every polygon can be turned into a square. He assumed that a polygon within a circle could no longer be distinguished from a circle after a certain number of sides and that the circle was therefore completely "exhausted".

With this idea, Eudoxos von Knidos developed the exhaustion method and thus calculated the volume of a pyramid and a cone. This method is called the exhaustion method (from exhaurire , Latin for “take out”, “exhaust”, “complete”).

The Greek scholar Archimedes (287–212 BC) adopted this method in 260 BC. And thus calculated the estimate and the definite integral of a parabola by means of a 96-point . ${\displaystyle 3+10/71<\pi }$

The process was an important integration process until the 17th century. Ludolph van Ceulen continued Archimedes' approach to the -Eck in a circle and was able to calculate pi up to 35 digits in 30 years of arithmetic work. ${\displaystyle 2^{62}}$

literature

• CH Edwards Jr .: The Historical Development of the Calculus , 1979, Springer New York