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Two-dimensional space

Index Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). [1]

106 relations: Analytic geometry, Angle, Area, Bijection, Cartesian coordinate system, Caspar Wessel, Circle, Clockwise, Complex plane, Conic section, Continuous function, Contractible space, Coordinate system, Coordinate vector, Coprime integers, Cross-polytope, Curve, Curve orientation, Decagon, Decagram (geometry), Digon, Dimension, Dodecagon, Dot product, Ellipse, Enneadecagon, Enneagram (geometry), Equilateral triangle, Euclid's Elements, Euclidean distance, Euclidean space, Field (mathematics), Frans van Schooten, Function (mathematics), Gradient, Gradient theorem, Graph (discrete mathematics), Graph embedding, Graph theory, Hendecagon, Heptadecagon, Heptagon, Heptagram, Hexadecagon, Hexagon, Hyperbola, Hypercube, Hypersphere, Icosagon, Integral, ..., Interior (topology), Jean-Robert Argand, Jordan curve theorem, La Géométrie, Line integral, Linear algebra, Ludwig Schläfli, Manifold, Mathematics, Monogon, Multiple integral, Nonagon, Number, Octadecagon, Octagon, Octagram, Open set, Origin (mathematics), Parabola, Parameter, Parametric equation, Partial derivative, Pentadecagon, Pentagon, Pentagram, Perpendicular, Piecewise, Pierre de Fermat, Planar graph, Plane (geometry), Plane curve, Point (geometry), Polar coordinate system, Projection (linear algebra), Pythagorean theorem, Rectangle, Regular polygon, Scalar field, Schläfli symbol, Sign (mathematics), Simplex, Simply connected space, Sphere, Square, Star polygon, Surface (topology), Tetradecagon, Topology, Torus, Tridecagon, Two-dimensional graph, Unit vector, Universe, Vector field, Vertex arrangement, Zeros and poles. Expand index (56 more) »

Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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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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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Caspar Wessel

Caspar Wessel (June 8, 1745, Vestby – March 25, 1818, Copenhagen) was a Danish–Norwegian mathematician and cartographer.

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A circle is a simple closed shape.

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Two-dimensional rotation can occur in two possible directions.

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Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Contractible space

In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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Coordinate vector

In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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Curve orientation

In mathematics, a positively oriented curve is a planar simple closed curve (that is, a curve in the plane whose starting point is also the end point and which has no other self-intersections) such that when traveling on it one always has the curve interior to the left (and consequently, the curve exterior to the right).

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In geometry, a decagon is a ten-sided polygon or 10-gon.

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Decagram (geometry)

In geometry, a decagram is a 10-point star polygon.

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In geometry, a digon is a polygon with two sides (edges) and two vertices.

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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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In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

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Dot product

In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.

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In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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In geometry an enneadecagon or 19-gon is a nineteen-sided polygon.

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Enneagram (geometry)

In geometry, an enneagram is a nine-pointed plane figure.

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Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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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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Frans van Schooten

Franciscus van Schooten (1615, Leiden – 29 May 1660, Leiden) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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In mathematics, the gradient is a multi-variable generalization of the derivative.

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Gradient theorem

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Graph embedding

In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of) are associated with edges in such a way that.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon.

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In geometry, a heptadecagon or 17-gon is a seventeen-sided polygon.

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In geometry, a heptagon is a seven-sided polygon or 7-gon.

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A heptagram, septagram, septegram or septogram is a seven-point star drawn with seven straight strokes.

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In mathematics, a hexadecagon (sometimes called a hexakaidecagon) or 16-gon is a sixteen-sided polygon.

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In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

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In geometry, an icosagon or 20-gon is a twenty-sided polygon.

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In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Interior (topology)

In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.

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Jean-Robert Argand

Jean-Robert Argand (July 18, 1768 – August 13, 1822) was an amateur mathematician.

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Jordan curve theorem

In topology, a Jordan curve, sometimes called a plane simple closed curve, is a non-self-intersecting continuous loop in the plane.

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La Géométrie

La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes.

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Line integral

In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.

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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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Ludwig Schläfli

Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces.

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In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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In geometry a monogon is a polygon with one edge and one vertex.

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Multiple integral

The multiple integral is a definite integral of a function of more than one real variable, for example, or.

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In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.

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A number is a mathematical object used to count, measure and also label.

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An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.

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In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

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In geometry, an octagram is an eight-angled star polygon.

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Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

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Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

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In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

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A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

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Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

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Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

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In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon.

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In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.

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In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

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In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain, a sub-domain.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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Plane curve

In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane.

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Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

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Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.

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In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

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A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Star polygon

In geometry, a star polygon is a type of non-convex polygon.

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.

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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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In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon.

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Two-dimensional graph

A two-dimensional graph is a set of points in two-dimensional space.

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Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

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The Universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

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Zeros and poles

In mathematics, a zero of a function is a value such that.

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[1] https://en.wikipedia.org/wiki/Two-dimensional_space

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