- This article is about the mathematician, not about his father, the economist Carl Menger.
He was the son of the famous economist Carl Menger.
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.