Method of exhaustion

The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will become arbitrarily small as n becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members.

The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a region by first comparing it to the area of a second region (which can be “exhausted” so that its area becomes arbitrarily close to the true area). The proof involves assuming that the true area is greater than the second area, and then proving that assertion false, and then assuming that it is less than the second area, and proving that assertion false, too.

The Method

The Method may refer to:

Science

The Method of Mechanical Theorems, a work of Archimedes

Arts and entertainment

The Method (album), a 1997 album by Killing Time

The Method (2005 film), a film by Marcelo Piñeyro

The Method (novel), a 2009 novel by Juli Zeh

Andwella or The Method, a band of UK/Irish origin

The Method, a band on the See Monkey Do Monkey record label

"The Method", a song by We Are Scientists from Safety, Fun, and Learning (In That Order)

Method acting

Stanislavski's system

Stanislavski's system

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Method of exhaustion

The Method

Science

Arts and entertainment

See also

How to Calculate Pi, Archimedes' Method

Finding Pi by Archimedes' Method