Method of exhaustion

The method of exhaustion is an ancient method for the calculation of surfaces, ie for integration.

Antiphon (430 BC) was convinced that we should be able to square a circle, since every polygon can be transformed into a square. He believed that one could not distinguish from the circle a polygon within a circle of a certain number of pages and the circle is thus " exhausted " completely.

With this idea, Eudoxus of Cnidus developed the method of exhaustion, and thus calculated the volume of a pyramid and a cone. This method is called exhaustion (of exhaurire, Latin for " take out ", " exhausted ", " complete ").

The Greek scholar Archimedes ( 287-212 BC) took up this method in 260 BC, and so calculated, by means of a 96 -gon, the estimation and the definite integral of a parabola.

The procedure was to the 17th century an important integration process. Ludolph van Ceulen continued the approach Archimedes ' to the corner in a circle and Pi could in 30 years of computing work so calculated to 35 digits.