Karl Menger

Karl Menger (Vienna, Austria, January 13, 1902 – Highland Park, Illinois, USA, October 5, 1985) was a mathematician of great scope and depth. Karl Menger, Mathematician File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Karl Menger, Mathematician File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Vienna (German: Wien ; Bosnian, Croatian, and Serbian: Beč, Czech: Vídeň, Hungarian: Bécs, Romanian: Viena, Romani: Bech or Vidnya, Russian: Вена, Slovak: Viedeň, Slovenian: Dunaj) is the capital of Austria, and also one of the nine States of Austria. ... January 13 is the 13th day of the year in the Gregorian calendar. ... 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ... Highland Park is a city located in Lake County, Illinois. ... October 5 is the 278th day of the year (279th in Leap years). ... This article is about the year. ... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ...

He was the illegitimate son of the famous economist Carl Menger. Austrian School economist Carl Menger Carl Menger Carl Menger (February 28, 1840 – February 26, 1921) was the founder of the Austrian School of economics. ...

He worked in mathematics on algebras, curve and dimension theory, and geometries. Moreover, he contributed to game theory and social sciences. He was a student of Hans Hahn and received his PhD from the University of Vienna in 1924. Brouwer invited Menger to teach at the University of Amsterdam in 1925, afterwards he returned to Vienna and obtained a professorship in 1928. From 1937 to 1946 he was professor for mathematics at the University of Notre Dame in Indiana (USA), from 1946 professor on the Illinois Institute of Technology in Chicago. Hans Hahn (1879 - 1934) was an Austrian mathematician who made many contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory. ... University of Vienna, main building, seen from Beethovens apartment The University of Vienna (German: Universität Wien) in Austria was founded in 1365 by Rudolph IV and hence named Alma mater Rudolphina. ... 1924 (MCMXXIV) was a leap year starting on Tuesday (link will take you to calendar). ... Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as L. E. J. Brouwer, was a Dutch mathematician, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis. ... From Athenaeum Illustre to University In January 1632 two internationally acclaimed scientists, Caspar Barlaeus and Gerardus Vossius, held their inaugural speech in the Athenaeum Illustre - the illustrious school - which had its seat in the 14th-century Agnietenkapel. ... 1925 (MCMXXV) was a common year starting on Thursday (link will take you to calendar). ... 1928 (MCMXXVIII) was a leap year starting on Sunday (link will take you to calendar). ... 1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar). ... 1946 (MCMXLVI) was a common year starting on Tuesday. ... The University of Notre Dame is a leading Roman Catholic institution of higher learning located in Notre Dame, Indiana, immediately northeast of South Bend, Indiana, United States. ... Official language(s) English Capital Indianapolis Largest city Indianapolis Area  Ranked 38th  - Total 36,418 sq. ... State Street Village, S.R. Crown Hall, Armour Main Building Illinois Institute of Technology (IIT) is a private Ph. ... Chicago (officially named the City of Chicago) is the third largest city in the United States (after New York City and Los Angeles), with an official population of 2,896,016, as of the 2000 census. ...

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. The Menger sponge is a fractal solid. ... Wacław Franciszek Sierpiński, was born on March 14, 1882 in Warsaw and died on October 21, 1969 in Warsaw. ... The Sierpinski carpet is a plane fractal first described by WacÅ‚aw SierpiÅ„ski. ... The Cantor set, introduced by German mathematician Georg Cantor, is a remarkable construction involving only the real numbers between zero and one. ...

Computer illustration of the "Menger sponge".

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. Image File history File links Please see the file description page for further information. ... Image File history File links Please see the file description page for further information. ... Arthur Cayley (August 16, 1821 - January 26, 1895) was a British mathematician. ... Distance Geometry is the characterization and study of sets based only on given values of the distance between member pairs. ...

The characteristic mathematical expressions appearing in those definitions are Cayley-Menger determinants. Distance geometry is the characterization and study of sets of points based only on given values of the distances between member pairs. ...

He also is credited with Menger's theorem. In the mathematical discipline of graph theory and related areas Mengers theorem is a basic result about connectivity in finite undirected graphs. ...

He was an active participant of the Vienna Circle which had discussions in the 1920s on social science and philosophy. During that time, he proved an important result on the St. Petersburg paradox with interesting applications to the utility theory in economics. Later he contributed to the development of game theory with Oskar Morgenstern. Moritz Schlick around 1930 The Vienna Circle (in German: der Wiener Kreis) was a group of philosophers who gathered around Moritz Schlick when he was called to the Vienna University in 1922, organized in a philosophical association named Verein Ernst Mach (Ernst Mach Society). ... In probability theory and decision theory the St. ... This article is about utility in economics and in game theory. ... Buyers bargain for good prices while sellers put forth their best front in Chichicastenango Market, Guatemala. ... Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ...

External links

• http://www.iit.edu/~am/Menger/menger.html