Karl Reinhardt (mathematician)

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Karl Reinhardt (born January 27, 1895 in Frankfurt am Main , † April 27, 1941 in Berlin ; full name: Karl August Reinhardt ) was a German mathematician.

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Reinhardt studied from 1913 at the University of Marburg (in addition to mathematics, also physics, chemistry, philosophy) and the Johann Wolfgang Goethe University in Frankfurt am Main , where he received his doctorate in 1918 under Ludwig Bieberbach on a problem of tiling ( on the decomposition of the plane in polygons ). According to Maier's obituary, he was also Hilbert's assistant in Göttingen during the First World War, where he worked as an assistant teacher. After the teaching degree, he was a trainee lawyer in Frankfurt am Main and a private teacher, before he became a research assistant in 1921 and ( Habilitation 1921, on images through analytical functions of two variables ) private lecturer at the University of Frankfurt. After a rehabilitation from 1924, he had a teaching position at the University of Greifswald , where he had been a full professor since 1928. He died of illness in 1941.

In 1928 he solved Hilbert's 18th problem of finding a polyhedron from which three-dimensional space can be built up without gaps and which is not the fundamental domain of a movement group. In 1932 Heinrich Heesch found such a solution for the plain as well.

He also dealt with the functional theory of several variables and in his habilitation in 1921 introduced Reinhardt's bodies in two complex dimensions, geometrically circular bodies in four-dimensional space. He then showed that the analogue of Riemann's mapping theorem (analytical mapping to circular areas in the plane) no longer exists in one complex dimension in two complex dimensions, but that the areas that can be mapped onto circular bodies are very limited.

His student Heinrich Voderberg (fallen in 1945) found a solution to a problem that Reinhardt (1934) considered unsolvable in the form of a triangle: to find flat paving stones (delimited in a straight line) that enclose a hole in one or two similar ( congruent) pavement fit, and with it the first spiral tiling. In his dissertation in 1933, his doctoral student Theodor Schmidt solved a conjecture by Hermann Minkowski about the filling of n-dimensional Euclidean spaces with cubes for dimensions less than or equal to eight (the general case was proved by György Hajós in 1941).

Reinhardt was a childhood friend of Wilhelm Süss and made it possible for him to do his habilitation with him in Greifswald (Süss was in Japan at the time) and to become a private lecturer.

Fonts

  • Methodical introduction to higher mathematics, Teubner 1934
  • On the calculation of probability, Greifswald, University Press L. Bamberg, 1936
  • For the treatment of integral calculus at the school, Greifswald, Universitätsverlag L. Bamberg

Web links

Individual evidence

  1. ↑ Online
  2. ↑ Reinhardt on the decomposition of the Euclidean spaces into congruent polytopes , session reports of the Prussian Academy of Sciences, 1928, pp. 150–155
  3. ↑ On mapping through analytical functions of two variables , Mathematische Annalen Vol. 83, 1921, p. 211, online
  4. ↑ Voderberg The decomposition of the surroundings of a flat area into congruent , annual report DMV, Vol. 36, 1936, p. 229
  5. ↑ Archived copy ( Memento of the original from March 5, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.uwgb.edu
  6. ^ Branko Grünbaum, GC Shephard: Tilings and Patterns, New York, 1987, ISBN 0-7167-1193-1 , Section 9.5, "Spiral Tilings," page 512.
  7. ^ Karl Theodor Schmidt, 1908–1986, 1944 adjunct professor for theoretical physics in Greifswald, later professor for physics in Freiburg im Breisgau. The Schmidt line comes from him .
  8. ^ John J. O'Connor, Edmund F. Robertson :  Karl Reinhardt (mathematician). In: MacTutor History of Mathematics archive .
personal data
SURNAME Reinhardt, Karl
ALTERNATIVE NAMES Reinhardt, Karl August
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH January 27, 1895
PLACE OF BIRTH Frankfurt am Main
DATE OF DEATH April 27, 1941
Place of death Berlin