In mathematics, the Menger sponge is a fractal curve. It is a universal curve, in that it has topological dimension one, and any other curve (more precisely: any compact metric space of topological dimension 1) is homeomorphic to some subset of it. It is sometimes called the Menger-Sierpinski sponge or the Sierpinski sponge. It is a three-dimensional extension of the Cantor set and Sierpinski carpet. It was first described by Karl Menger (1926) while exploring the concept of topological dimension.
The Menger sponge simultaneously exhibits an infinite surface area and encloses zero volume.
Read more about Menger Sponge: Construction, Properties, Formal Definition
Famous quotes containing the word sponge:
“He who has been impoverished for a long time ... who has long stood before the door of the mighty in darkness and begged for alms, has filled his heart with bitterness so that it resembles a sponge full of gall; he knows about the injustice and folly of all human action and sometimes his lips tremble with rage and a stifled scream.”
—Stefan Zweig (18811942)