Johannes Hjelmslev
Encyclopedia
Johannes Trolle Hjelmslev (7 April 1873 – 16 February 1950) was a mathematician from Copenhagen
, Denmark
. Hjelmslev worked in geometry
and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation
, a method for mapping
an entire hyperbolic plane
into a circle
with a finite radius
.
He was the father of Louis Hjelmslev
.
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
. Hjelmslev worked in geometry
Geometry
Geometry 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 ....
and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation
Hjelmslev transformation
In mathematics, the Hjelmslev transformation is an effective method for mapping an entire hyperbolic plane into a circle with a finite radius. The transformation was invented by Danish mathematician Johannes Hjelmslev...
, a method for mapping
Map (mathematics)
In most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.In graph theory, a map is a...
an entire hyperbolic plane
Hyperbolic space
In mathematics, hyperbolic space is a type of non-Euclidean geometry. Whereas spherical geometry has a constant positive curvature, hyperbolic geometry has a negative curvature: every point in hyperbolic space is a saddle point...
into a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
with a finite radius
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
.
He was the father of Louis Hjelmslev
Louis Hjelmslev
Louis Hjelmslev was a Danish linguist whose ideas formed the basis of the Copenhagen School of linguistics. Born into an academic family , Hjelmslev studied comparative linguistics in Copenhagen, Prague and Paris...
.
Publications
- Johannes Hjelmslev, Darstellende Geometrie, Teubner 1914
- Johannes Hjelmslev, Geometrische Experimente, Teubner 1915
- 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
External links
- Salmonsens Konversationsleksikon, http://runeberg.org/salmonsen/2/11/0531.html
- Salmonsens Konversationsleksikon, http://runeberg.org/salmonsen/2/26/0514.html