Johannes Hjelmslev

John Trolle Hjelmslev, born as John Petersen ( born April 7, 1873 in Horning, † February 16, 1950 in Copenhagen) was a Danish mathematician who worked on geometry.

He initially published under his birth name J. Petersen and called himself later Hjelmslev.

Life and work

Hjelmslev studied in Copenhagen, where he graduated in 1894 and in 1897 made ​​his doctorate. From 1903 he was a lecturer and in 1905 professor of descriptive geometry at the Technische Hochschule ( Polyteknisk Laereanstalt ) Copenhagen and from 1917 professor at the University of Copenhagen, where he officiated in the academic year 1928/29, as rector.

Hjelmslev introduced new geometric construction problems one ( described in his book " Geometric experiments") and dealt with the special geometries that result from relaxations of the axioms of Euclidean geometry.

He is considered the founder of the reflection geometry: In 1907, he developed the planar geometry of absolute reflection axioms. This is by Friedrich Bachmann and others have been taken up and developed later. Max Dehn in 1926 called this axiomatic justification of absolute geometry by Hjelmslev the highest point reaches the modern mathematics Euclid also going in the grounds of elementary geometry.

In works from 1929, he developed a general Kongruenzlehre in which he loosened further axioms such as the arrangement and incidence. A motive was that he so wanted to wear the ideological "fuzziness " of points account. He was so beside D. Barbilian one of the founders of the ring geometry ( geometry over rings ), in Hjelmslev's case using the ring of dual numbers.

With named after him Hjelmslev transformation, the hyperbolic plane can be mapped into a circle. After him also Hjelmslev groups and levels are named ( in which more than one can go straight through two points).

In the history of mathematics, he explored Georg Mohr (1640-1697), author of " Euclides danicus " (Amsterdam 1672), and gave him in 1928 reissued.

He is the father of the linguist Louis Hjelmslev (1899-1965), a professor in Copenhagen.

Writings

  • Descriptive Geometry, Teubner 1914
  • Foundations of projective geometry, 1929 ( Danish)
  • The natural geometry - four lectures, Hamburg Mathematical monographs 1923
  • Geometric experiments, Teubner 1915
  • Contributions to the biography of Georg Mohr, Det Royal Danish Videnskabernes Selskab, Math - Fys. Meddelelser, Bd.11, 1931, No.4
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