The
method of exhaustion (, or ) 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.