Johannes Trolle Hjelmslev (; 7 April 1873 – 16 February 1950) was a mathematician from

Hørning Hørning is a town in central Denmark with a population of 8,542 (1 January 2025),Denmark Denmark is a Nordic countries, Nordic country in Northern Europe. It is the metropole and most populous constituent of the Kingdom of Denmark,, . also known as the Danish Realm, a constitutionally unitary state that includes the Autonomous a ...

. Hjelmslev worked in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

and

history of geometry Geometry (from the ; '' geo-'' "earth", '' -metron'' "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmeti ...

. He was the discoverer and eponym of the

Hjelmslev transformation In mathematics, the Hjelmslev transformation is an effective method for Map (mathematics), mapping an entire Hyperbolic space, hyperbolic plane into a circle with a finite radius. The transformation was invented by Danish mathematician Johannes Hj ...

, a method for mapping an entire

hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P' ...

into a

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

with a finite

radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...

. He was the father of

Louis Hjelmslev Louis Trolle Hjelmslev (; 3 October 189930 May 1965) was a Danish linguist whose ideas formed the basis of the Copenhagen School of linguistics. Born into an academic family (his father was the mathematician Johannes Hjelmslev), Hjelmslev studi ...

. Originally named Johannes Trolle Petersen, he changed his patronymic to the surname Hjelmslev to avoid confusion with

Julius Petersen Julius Peter Christian Petersen (16 June 1839 in Sorø, West Zealand – 5 August 1910 in Copenhagen) was a Denmark, Danish mathematician. His contributions to the field of mathematics led to the birth of graph theory. Biography Petersen's in ...

. Some of his results are known under his original name, including the

Petersen–Morley theorem In geometry, the Petersen–Morley theorem states that, if , , are three general skew lines In three-dimensional geometry, skew lines are two Line (geometry), lines that do not Line-line intersection, intersect and are not Parallel (geometry), p ...

Publications

*Johannes Hjelmslev, ''Grundprinciper for den infinitesimale Descriptivgeometri med Anvendelse paa Læren om variable Figurer. Afhandling for den philosophiske Doctorgrad'', 1897 *Johannes Hjelmslev, ''Deskriptivgeometri: Grundlag for Forelæsninger paa Polyteknisk Læreanstalt'', Jul. Gjellerup 1904 *Johannes Hjelmslev
''Geometriske Eksperimenter''
Jul. Gjellerup 1913 *Johannes Hjelmslev
''Darstellende Geometrie'', Teubner 1914
*Johannes Hjelmslev, ''Geometrische Experimente'', Teubner 1915 *Johannes Hjelmslev, ''Lærebog i Geometri til Brug ved den Polytekniske Læreanstalt'', Jul. Gjellerup 1918 *Johannes Hjelmslev
''Die natürliche Geometrie- vier Vorträge'', Hamburger Mathematische Einzelschriften 1923
*Johannes Hjelmslev, Om et af den danske matematiker Georg Mohr udgivet skrift ''Euclides Danicus'', udkommet i Amsterdam i 1672", ''Matematisk Tidsskrift'' B, 1928, pp 1-7 *Johannes Hjelmslev, Grundlagen der projektiven Geometrie, 1929 *Johannes Hjelmslev, Beiträge zur Lebensbeschreibung von Georg Mohr, Det Kongelige Danske Videnskabernes Selskab, Math.-Fys. Meddelelser, Bd.11, 1931, Nr.4 *Johannes Hjelmslev, ''Grundlag for den projektive Geometri'', Gyldendal 1943

References

* *Gottwald, Ilgauds, Schlote ''Lexikon bedeutender Mathematiker'', Leipzig 1990

External links

*''Salmonsens Konversationsleksikon''

*''Salmonsens Konversationsleksikon''

{{DEFAULTSORT:Hjelmslev, Johannes Trolle 1873 births 1950 deaths 20th-century Danish mathematicians Geometers People from Skanderborg Municipality Academic staff of the University of Copenhagen Rectors of the University of Copenhagen Members of the Royal Society of Sciences in Uppsala

Publications

See also

References

External links