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:
“Alas for the affairs of men! When they are fortunate you might compare them to a shadow; and if they are unfortunate, a wet sponge with one dash wipes the picture away.”
—Aeschylus (525–456 B.C.)