Editing Karl Menger (section)

==Contributions to mathematics==
[[Image:Menger sponge (IFS).jpg|thumb|Computer illustration of the "Menger sponge".]]
His most famous popular contribution was the [[Menger sponge]] (mistakenly known as [[Waclaw Sierpinski|Sierpinski]]'s sponge), a three-dimensional version of the [[Sierpinski carpet|Sierpiński carpet]]. It is also related to the [[Cantor set]].

With [[Arthur Cayley]], Menger is considered one of the founders of [[distance geometry]]; especially by having formalized definitions of 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 determinant]]s.

He was an active participant of the [[Vienna Circle]], which had discussions in the 1920s on social science and philosophy. During that time, he published an influential result<ref>{{Cite journal|last=Menger|first=Karl|date=1934-08-01|title=Das Unsicherheitsmoment in der Wertlehre|journal=Zeitschrift für Nationalökonomie|language=de|volume=5|issue=4|pages=459–485|doi=10.1007/BF01311578|s2cid=151290589|issn=1617-7134}}</ref> on the [[St. Petersburg paradox#Expected utility theory|St. Petersburg paradox]] with applications to the [[utility theory]] in [[economics]]; this result has since been criticised as fundamentally misleading.<ref>Peters, O. and Gell-Mann, M., 2016. Evaluating gambles using dynamics. ''Chaos: An Interdisciplinary Journal of Nonlinear Science'', 26(2), p.023103</ref> Later he contributed to the development of [[game theory]] with [[Oskar Morgenstern]].

Meneger's work on [[topology without points]] followed [[Arthur Eddington]]'s approach to geometry without points.
<ref>Menger, Karl, "Topology without points." Rice Institute Pamphlet - Rice University Studies, 27, no. 1 (1940) Rice University [https://repository.rice.edu/items/aa654487-128a-4379-9108-9ed1b798e01b]</ref>

Menger was a founding member of the [[Econometric Society]].