Benz plane
Encyclopedia
In mathematics
, a Benz plane is a type of 2-dimension
al geometrical
structure, named after the German
mathematician
Walter Benz
. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced separately: Möbius plane
s, Laguerre planes, and Minkowski plane
s.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a Benz plane is a type of 2-dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
al geometrical
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 ....
structure, named after the German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Walter Benz
Walter Benz
Walter Benz is a German mathematician, an expert in geometry.Benz studied at the Johannes Gutenberg University of Mainz and received his doctoral degree in 1954, with Robert Furch as his advisor....
. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced separately: Möbius plane
Möbius plane
A Möbius plane or inversive plane is a particular kind of plane geometry, built upon some affine planes by adding one point, called the ideal point or point at infinity. In a Möbius plane straight lines are a special case of circles; they are the circles that pass through the ideal point. Möbius...
s, Laguerre planes, and Minkowski plane
Minkowski plane
In mathematics, the Minkowski plane is a two-dimensional affine space provided with a metric that is invariant under translations.Often one identifies the underlying affine space with the plane R2....
s.