Hugo Hadwiger
Hugo Hadwiger (born December 23, 1908 in Karlsruhe , † October 29, 1981 in Bern ) was a Swiss mathematician who dealt with integral geometry , convex and combinatorial geometry and graph theory.
Hadwiger studied mathematics, physics and insurance theory in Bern and Hamburg from 1929 to 1935 (in 1935 with Wilhelm Blaschke ) and received his doctorate in Bern in 1934 ( rearrangement of series of analytical functions ). In 1936 he completed his habilitation and was then a private lecturer at the University of Bern , from 1937 associate professor and from 1945 until his retirement in 1977 full professor. In 1947/48 and 1960/61 he was dean of the mathematics faculty there.
Hadwiger is best known for his studies on geometric measurement theory ( Hadwiger's theorem in integral geometry ). In addition, he improved the solution of Hilbert's 3rd problem by Max Dehn by generalizing his criterion for the equal decomposition of polyhedra from three to higher dimensions. Dehn had shown for three dimensions that there are polyhedra of the same volume that are not identical in decomposition, which put a stop to the elementary geometric foundation of the volume. Hadwiger simplified Dehn's opaque and complicated proof again.
In 1943, in graph theory, he formulated an unresolved conjecture about the coloration of graphs, which is based on the four-color theorem : If the corners of an undirected graph can only be colored with at least k colors so that no two connected corner points have the same color, then there are k disjoint connected subgraphs, which are all connected in pairs by at least one edge ( Hadwinger's conjecture ).
During the Second World War he worked on the modification of the Swiss version of the Enigma encryption machine , the Enigma-K model, and based on this he developed the Nema (new machine).
His doctoral students include Jürg Rätz and Arnold Kirsch .
See also
Fonts
- Lectures on content, surface and isoperimetry. Springer, Basic Teachings of Mathematical Sciences, 1957.
- Old and new about convex bodies. Birkhäuser 1955.
- About a classification of the route complexes. Quarterly journal of the Natural Research Society Zurich, Vol. 88, 1943, pp. 133–143 (Hadwinger's assumption in graph theory).
- With H. Debrunner, V. Klee: Combinatorial geometry in the plane. Holt, Rinehart and Winston, New York 1964.
- To the problem of the equality of decomposition of k-dimensional polyhedra. Mathematische Annalen, Vol. 127, pp. 170-174 (1954).
- Supplementary equality of k-dimensional polyhedra. Math. Journal, Vol. 55, Issue 3, pp. 292-298 (1952).
- Linear additive polyhedron functionals and equality of decomposition. Math. Zeitschrift, Vol. 58, pp. 4-14 (1953).
- With Paul Glur: Equal decomposition of plane polygons. Elements of Mathematics, Vol. 6, No. 5, pp. 97-106 (1951).
Notes and references
- ^ The lecturers at the Bern University from 1980 to today. At: uniarchiv.unibe.ch. (PDF; 516 kB). June 8, 2009, accessed February 11, 2012.
- ↑ Jürg Rätz: In memory of Prof. Hugo Hadwiger. In: DerBund.ch. December 23, 2008, accessed February 11, 2012.
- ↑ In two dimensions, on the other hand, equality of decomposition is equivalent to equality of volume, as Wolfgang Bolyai and Paul Gerwien showed in 1833, see Bolyai-Gerwien theorem .
- ↑ Weniamin Kagan had already simplified it before . A representation can be found in Aigner, Ziegler: Proofs from the Book. Springer 1998, chapter 7.
- ↑ Hugo Hadwiger in the Mathematics Genealogy Project (English)
personal data | |
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SURNAME | Hadwiger, Hugo |
BRIEF DESCRIPTION | Swiss mathematician |
DATE OF BIRTH | December 23, 1908 |
PLACE OF BIRTH | Karlsruhe |
DATE OF DEATH | October 29, 1981 |
Place of death | Bern |