method of exhaustion


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method of exhaustion

[‚meth·əd əv ig′zȯs·chən]
(mathematics)
A method of finding areas and volumes by finding an increasing or decreasing sequence of sets whose areas or volumes are known and less than or greater than the desired area or volume, and then showing that the area or volume between the boundaries of the approximating sets and the boundary of the set to be measured approaches zero (is exhausted).
References in periodicals archive ?
Fairly early in the section, Lockhart introduces the so-called classical "method of exhaustion," "by far the most powerful and flexible measuring technique ever devised" (p.
He also uses the method of exhaustion to argue for the validity of Cavalieri's Principle, which compares lower-dimensional cross sections of figures in order to relate an unknown measure (area, volume) to one that's already known.
It was Archimedes who laid the foundations for what we know today as integral calculus, in his development of the "method of exhaustion".

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