# Karl Menger

*This article is about the mathematician, not about his father, the economist Carl Menger.*

**Karl Menger** (born in Vienna, Austria, January 13 1902 -- died in Highland Park, Illinois, USA, October 5 1985) was a mathematician of great scope and depth.

He was the son of the famous economist Carl Menger.

He did work on algebras, curve and dimension theory, and geometries. He was a student of Hans Hahn and received his PhD from the University of Vienna in 1924.

His most famous popular contribution was the Menger sponge (mistakenly known as Sierpinski's sponge), a three-dimensional version of Sierpinski's carpet. It is also related to the Cantor set and the Sierpinski square.

With Arthur Cayley, Menger is considered one of the founders of distance geometry; especially by having formalized definitions to the notions of *angle* and of *curvature* in terms of directly measurable physical quantities, namely ratios of *distance* values.

The characteristic mathematical expressions appearing in those definitions are Cayley-Menger determinants.

He also is credited with Menger's theorem.