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82 relations: Affine plane (incidence geometry), Algebraic geometry, Alternative algebra, American Journal of Mathematics, American Mathematical Monthly, Associative property, Automorphic function, Automorphism, Bijection, Block design, Bruck–Ryser–Chowla theorem, Cartesian product, Cayley plane, Collineation, Combinatorial design, Commutative property, Complex number, Complex projective plane, Converse relation, David Hilbert, Desargues's theorem, Division ring, Duality (projective geometry), Elliptic geometry, Equivalence relation, Ergebnisse der Mathematik und ihrer Grenzgebiete, Fano plane, Field (mathematics), Finite field, Finite geometry, Galois geometry, Gaston Tarry, General linear group, Gino Fano, Girard Desargues, Graeco-Latin square, Grassmannian, Group (mathematics), Homography, Hughes plane, Incidence (geometry), Incidence matrix, Incidence structure, Integer, Involution (mathematics), John Playfair, Leonhard Euler, Line at infinity, Manifold, Mathematics, ..., Modular arithmetic, Moufang plane, Moulton plane, Non-Desarguesian plane, Octonion, Pappus's hexagon theorem, Parallel (geometry), Perspective (graphical), Planar ternary ring, Plane (geometry), Point at infinity, Primitive notion, Product topology, Projective geometry, Projective linear group, Projective space, Quaternionic projective space, Quotient space (topology), Raj Chandra Bose, Real number, Real projective plane, Smooth projective plane, Springer Science+Business Media, Steiner system, Subspace topology, Symmetry, Thirty-six officers problem, Topological space, Topology, Transactions of the American Mathematical Society, Vector space, Wedderburn's little theorem. Expand index (32 more) »
Affine plane (incidence geometry)
In geometry, an affine plane is a system of points and lines that satisfy the following axioms.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Alternative algebra
In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.
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American Journal of Mathematics
The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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Automorphic function
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Block design
In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application.
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Bruck–Ryser–Chowla theorem
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of block designs.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Cayley plane
In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions.
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Collineation
In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear.
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Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complex projective plane
In mathematics, the complex projective plane, usually denoted P2(C), is the two-dimensional complex projective space.
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Converse relation
In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.
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David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
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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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Duality (projective geometry)
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept.
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Elliptic geometry
Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Ergebnisse der Mathematik und ihrer Grenzgebiete
Ergebnisse der Mathematik und ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics is a series of scholarly monographs published by Springer Science+Business Media.
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Fano plane
In finite geometry, the Fano plane (after Gino Fano) is the finite projective plane of order 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 when they are applied to rational and real numbers.
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Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
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Finite geometry
A finite geometry is any geometric system that has only a finite number of points.
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Galois geometry
Galois geometry (so named after the 19th century French Mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or Galois field).
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Gaston Tarry
Gaston Tarry (27 September 1843 – 21 June 1913) was a French mathematician.
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General linear group
In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.
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Gino Fano
Gino Fano (5 January 18718 November 1952) was an Italian mathematician, best known as the founder of finite geometry.
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Girard Desargues
Girard Desargues (21 February 1591 – September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry.
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Graeco-Latin square
In combinatorics, a Graeco-Latin square or Euler square or orthogonal Latin squares of order n over two sets S and T, each consisting of n symbols, is an n×n arrangement of cells, each cell containing an ordered pair (s,t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells contain the same ordered pair.
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Grassmannian
In mathematics, the Grassmannian is a space which parametrizes all -dimensional linear subspaces of the n-dimensional vector space.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Homography
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.
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Hughes plane
In mathematics, a Hughes plane is one of the non-Desarguesian projective planes found by.
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Incidence (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.
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Incidence matrix
In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects.
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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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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
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John Playfair
Rev Prof John Playfair FRSE, FRS (10 March 1748 – 20 July 1819) was a Church of Scotland minister, remembered as a scientist and mathematician, and a professor of natural philosophy at the University of Edinburgh.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Line at infinity
In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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Moufang plane
In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically it is a special type of translation plane.
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Moulton plane
In incidence geometry, the Moulton plane is an example of an affine plane in which Desargues's theorem does not hold.
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Non-Desarguesian plane
In mathematics, a non-Desarguesian plane, named after Girard Desargues, is a projective plane that does not satisfy Desargues' theorem, or in other words a plane that is not a Desarguesian plane.
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Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.
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Pappus's hexagon theorem
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.
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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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Perspective (graphical)
Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.
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Planar ternary ring
In mathematics, an algebraic structure (R,T) consisting of a non-empty set R and a ternary mapping T \colon R^3 \to R \, may be called a ternary system.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Point at infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
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Primitive notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept.
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Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
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Projective geometry
Projective geometry is a topic in mathematics.
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Projective linear group
In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V).
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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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Quaternionic projective space
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by and is a closed manifold of (real) dimension 4n.
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Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
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Raj Chandra Bose
Raj Chandra Bose (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.
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Smooth projective plane
In geometry, smooth projective planes are special projective planes.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Steiner system
The Fano plane is an S(2,3,7) Steiner triple system. The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ.
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Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Thirty-six officers problem
The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Transactions of the American Mathematical Society
The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Wedderburn's little theorem
In mathematics, Wedderburn's little theorem states that every finite domain is a field.
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Redirects here:
Baer subplane, Desargues plane, Desarguesian plane, Finite projective plane, Projective Plane.
References
[1] https://en.wikipedia.org/wiki/Projective_plane
