Incidence (geometry) and Projective geometry

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Difference between Incidence (geometry) and Projective geometry

Incidence (geometry) vs. Projective geometry

In geometry, an incidence relation is a binary relation between different types of objects 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. Projective geometry is a topic in mathematics.

Axiom

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

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Desargues's theorem

In projective geometry, Desargues's theorem, named after Girard Desargues, states: Denote the three vertices of one triangle by and, and those of the other by and.

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Division ring

In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.

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Incidence geometry

In mathematics, incidence geometry is the study of incidence structures.

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Incidence structure

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

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

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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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Projective range

In mathematics, a projective range is a set of points in projective geometry considered in a unified fashion.

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Projective space

In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.

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Synthetic geometry

Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.

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