Karl Menger facts for kids
Quick facts for kids
Karl Menger
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| Born | January 13, 1902 |
| Died | October 5, 1985 (aged 83) Highland Park, Illinois, USA
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| Nationality | Austrian |
| Alma mater | University of Vienna (PhD, 1924) |
| Known for | Menger characterization theorem Menger curvature Menger space Menger sponge Menger's theorem Menger–Nöbeling theorem Cayley–Menger determinant |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Illinois Institute of Technology University of Notre Dame University of Vienna |
| Thesis | Über die Dimensionalität von Punktmengen (1924) |
| Doctoral advisor | Hans Hahn |
| Doctoral students | Abraham Wald Witold Hurewicz Georg Nöbeling |
Karl Menger (born January 13, 1902 – died October 5, 1985) was a brilliant mathematician. He was born in Austria and later became an American citizen. His father, Carl Menger, was a famous economist. Karl Menger studied many different areas of mathematics. He worked on how shapes and spaces are measured. He also made important contributions to game theory, which is about making smart decisions.
Contents
About Karl Menger's Life
Karl Menger earned his PhD in 1924 from the University of Vienna. His teacher was Hans Hahn. In 1925, he was invited to teach at the University of Amsterdam. He returned to Vienna in 1927 to become a professor there.
Teaching in the United States
Menger visited Harvard University and the Rice Institute in 1930 and 1931. From 1937 to 1946, he was a professor at the University of Notre Dame. Later, from 1946 to 1971, he taught at the Illinois Institute of Technology (IIT) in Chicago. IIT honored him with a special degree in 1983.
Karl Menger's Math Discoveries
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One of his most famous creations is the Menger sponge. This is a cool three-dimensional shape. It looks like a sponge with many holes. It's similar to the Sierpinski carpet and the Cantor set. These are all examples of complex shapes called fractals.
Measuring Shapes and Spaces
Karl Menger is known as one of the people who started distance geometry. This is a way to define angles and curves using distances. Imagine you want to measure an angle. Menger found ways to do this using only how far apart points are. He used special math expressions called Cayley–Menger determinants for these measurements.
Working with the Vienna Circle
Menger was also part of a group called the Vienna Circle in the 1920s. They discussed ideas about social science and philosophy. He also worked on game theory with Oskar Morgenstern. Game theory helps us understand how people make choices when they interact. Menger was also a founding member of the Econometric Society. This group studies how math can be used in economics.
Karl Menger's Lasting Impact
Karl Menger's longest teaching job was at the Illinois Institute of Technology (IIT). Today, IIT holds an annual lecture series named after him. They also give the IIT Karl Menger Student Award. This award goes to an outstanding student each year.
See also
- Distance geometry
- Kuratowski's theorem
- Selection principle
- Travelling salesman problem
