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Benz plane, the Glossary

In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz.^[1]

27 relations: Axiomatic system, Conformal geometry, Conic section, Cross section (geometry), Dimension, Elsevier, Encyclopedia of Mathematics, Euclidean plane, Field (mathematics), Geometry, Germany, Incidence (geometry), Incidence structure, Intersection, Laguerre plane, Laguerre transformations, Mathematician, Mathematics, Möbius plane, Minkowski plane, Projective plane, Quadric, Real number, Springer Science+Business Media, Stereographic projection, Technische Universität Darmstadt, Walter Benz.
Planes (geometry)

Axiomatic system

In mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems.

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Conformal geometry

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.

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Conic section

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

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In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Benz plane and cross section (geometry) are planes (geometry).

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Elsevier

Elsevier is a Dutch academic publishing company specializing in scientific, technical, and medical content.

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Encyclopedia of Mathematics

The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.

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Euclidean plane

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.

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Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

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Germany

Germany, officially the Federal Republic of Germany (FRG), is a country in Central Europe.

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Incidence (geometry)

In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used.

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Incidence structure

In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects.

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Intersection

In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously.

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Laguerre plane

In mathematics, a Laguerre plane is one of the three types of Benz plane, which are the Möbius plane, Laguerre plane and Minkowski plane. Benz plane and Laguerre plane are planes (geometry).

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Laguerre transformations

The Laguerre transformations or axial homographies are an analogue of Möbius transformations over the dual numbers.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Möbius plane

In mathematics, the classical Möbius plane (named after August Ferdinand Möbius) is the Euclidean plane supplemented by a single point at infinity. Benz plane and Möbius plane are planes (geometry).

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Minkowski plane

In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane). Benz plane and Minkowski plane are planes (geometry).

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Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane.

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Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).

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Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

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Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Stereographic projection

In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point.

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Technische Universität Darmstadt

The Technische Universität Darmstadt (official English name Technical University of Darmstadt, sometimes also referred to as Darmstadt University of Technology), commonly known as TU Darmstadt, is a research university in the city of Darmstadt, Germany.

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Walter Benz

Walter Benz (May 2, 1931 Lahnstein – January 13, 2017 Ratzeburg) was a German mathematician, an expert in geometry.

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References

[1] https://en.wikipedia.org/wiki/Benz_plane

Also known as Benz planes, Ebene Kreisgeometrien.