Hugo Hadwiger

Hugo Hadwiger ( born December 23, 1908 in Karlsruhe, † October 29, 1981 in Bern ) was a Swiss mathematician who worked on integral geometry, convex and combinatorial geometry and graph theory.

Hadwiger studied from 1929 to 1935 Mathematics, Physics and Actuarial Science in Bern and Hamburg (1935 Wilhelm Blaschke ) and in 1934 in Bern doctorate ( reordering of rows of analytic functions ). In 1936 he qualified as a professor and then was a lecturer at the University of Bern in 1937 and an associate from 1945 until his retirement in 1977 full professor. 1947/48 and 1960/61, he was dean of the mathematics department.

Hadwiger is mainly due to the geometric measure theory studies known ( Hadwigers theorem in integral geometry ). He also improved the solution of Hilbert's third problem by Max Dehn, by the generalized criterion for the decomposition of equality of polyhedra from three to higher dimensions. Dehn had shown for three dimensions, there are polyhedra of equal volume that are not equidecomposable what the elementary geometric reasoning of the volume has put a stop. Hadwiger simplified so that the opaque and complicated proof of Dehn again.

In graph theory, he formulated 1943 until today unsolved conjecture on colorings of graphs inspired by the four- color theorem: Are the corners ( vertices ) of an undirected graph with at least k colors colorable ( so that no two connected vertices of the same color have ), there are k disjoint connected subgraph which are connected to each other by at least one edge ( Hadwigers guess).

During the Second World War, he worked on the modification of the Swiss version of the Enigma decoding machine ( called NEMA, for New machine ).

Writings

  • Lectures on content, surface and Isoperimetrie, Springer, basic teachings of Mathematical Sciences, 1957
  • Old and New on convex bodies, Birkhauser 1955
  • "On a classification of route Complex ", Quarterly magazine of Natural History Society Zurich, Vol 88, 1943, pp. 133-143 ( Hadwigers conjecture in graph theory )
  • On the problem of decomposing equality k -dimensional polyhedra, Mathematische Annalen Bd.127, 1954, p.170
  • Supplement equality k -dimensional polyhedron, Math Journal, Vol 55, 1952, pp. 292-298.
  • Linear additive decomposition Polyederfunktionale and equality, Math Z., Vol 58, 1953, p.4 - 14th
  • With Paul Glur decomposition of planar polygons equality, Elements of Math, Vol. 6, 1951, p.97 -106

Notes and references

  • Mathematicians ( 20th century)
  • Graph theorists
  • Swiss
  • Born in 1908
  • Died in 1981
Hadwiger conjecture (graph theory) Der Bund Wallace–Bolyai–Gerwien theorem Proofs from THE BOOK Integrated Authority File
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