The Menger sponge is a three-dimensional fractal curve that exhibits infinite surface area and zero volume. This shows the POV-Ray code to render this mathematical structure
Karl Menger was an Austrian-American mathematician working on the algebra of geometries, curve and dimension theory. Menger was born in Vienna in 1902 to economist Carl Menger and novelist Hermione Andermann.
In 1920, Karl Menger enrolled at the University of Vienna to study Physics and attended lectures by Hans Hahn. Hahn lectured on a problem of defining the concept of a curve, at the time considered unsolvable. Part-way through his studies, Menger had developed a full theory of curves and earned his doctorate with Hahn.
Menger thought about geometry in its most fundamental sense and devised a completely new approach to Euclidean geometry. One of his important contributions to geometry was the discovery of a 'universal curve' in three-dimensional space, known now as the Menger Sponge.
This sponge has the property that every concievable curve can be embedded within it.
