Mathematics-Online lexicon: Approximation of Volume

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	Mathematics-Online lexicon:
	Approximation of Volume

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

For a regular region

the volume can be defined by approximation using a sequence of polygonal regions

with $\operatorname{dist}_H (V_n,V)\to 0$ :

$\displaystyle \operatorname{vol} V = \lim_{n\to\infty} \operatorname{vol} V_n \,.$

The limit exists because of the piecewise continuity of the boundary curves of

and it is independent from the chosen sequence

(Authors: Höllig/Streit/Höfert)

Example:

automatically generated 8/ 4/2008