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Curve

Index Curve

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. [1]

126 relations: Algebraic curve, Algebraic equation, Algebraic geometry, Algebraic variety, Algebraically closed field, American Mathematical Society, Analytic geometry, Angle trisection, Apollonius of Perga, Archimedean spiral, Archimedes, Astronomy, Atlas (topology), Bézout's theorem, Bijection, Brachistochrone curve, Calculus of variations, Catenary, Characteristic (algebra), Cissoid of Diocles, Classical mechanics, Compass-and-straightedge construction, Complete intersection, Complex analysis, Complex number, Conchoid (mathematics), Conic section, Connected space, Continuous function, Coordinate system, Cryptography, Cubic plane curve, Curvature, Curve fitting, Curve orientation, Curve sketching, Cusp (singularity), Cycloid, Derivative, Dictionary.com, Diffeomorphism, Differentiable function, Differentiable manifold, Differential calculus, Differential geometry, Differential geometry of curves, Dimension of an algebraic variety, Diocles (mathematician), Doubling the cube, Dragon curve, ..., Elimination theory, Elliptic curve, Equivalence class, Equivalence relation, Euclid, Euclid's Elements, Euclidean space, Fermat curve, Fermat's Last Theorem, Gallery of curves, General relativity, General topology, Genus (mathematics), Graph of a function, Hausdorff dimension, Helix, Homeomorphism, Homogeneous polynomial, Implicit curve, Injective function, Interval (mathematics), Inverse function, Johannes Kepler, Jordan curve theorem, Koch snowflake, Lebesgue measure, Line (geometry), Linearity, Lipschitz continuity, List of curves, List of curves topics, List of geometers, Manifold, Mathematics, Metric derivative, Metric space, Nicomedes (mathematician), Number theory, Osculating circle, Parabola, Parametric surface, Parametrization, Path (topology), Peano curve, Perseus (geometer), Phillips curve, Piecewise, Plane curve, Position (vector), Power series, Projective geometry, Projective plane, Rational number, Real algebraic geometry, Real number, Riemann surface, Set (mathematics), Sign (mathematics), Singular point of a curve, Smoothness, Space-filling curve, Spacetime, Spiric section, Square, Squaring the circle, Tautochrone curve, Thomas Little Heath, Topological space, Topology, Torus, Transcendental curve, Two-dimensional graph, Two-dimensional space, Vector-valued function, Winding number, World line. Expand index (76 more) »

Algebraic curve

In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry.

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Algebraically closed field

In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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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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Angle trisection

Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.

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Apollonius of Perga

Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.

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Archimedean spiral

The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd century BC Greek mathematician Archimedes.

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Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Astronomy

Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

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Atlas (topology)

In mathematics, particularly topology, one describes a manifold using an atlas.

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Bézout's theorem

Bézout's theorem is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves which do not share a common component (that is, which do not have infinitely many common points).

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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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Brachistochrone curve

In mathematics and physics, a brachistochrone curve, or curve of fastest descent, is the one lying on plane between a point A and a lower point B, where B is not directly below A, on which a bead slides frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time.

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Calculus of variations

Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

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Catenary

In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.

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Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.

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Cissoid of Diocles

In geometry, the cissoid of Diocles is a cubic plane curve notable for the property that it can be used to construct two mean proportionals to a given ratio.

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Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

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Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

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Complete intersection

In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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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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Conchoid (mathematics)

A conchoid is a curve derived from a fixed point O, another curve, and a length d. It was invented by the ancient Greek mathematician Nicomedes.

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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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Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

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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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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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Cryptography

Cryptography or cryptology (from κρυπτός|translit.

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Cubic plane curve

In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation.

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Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

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Curve fitting

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.

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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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Curve sketching

In.

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Cusp (singularity)

In mathematics a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point on the curve must start to move backward.

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Cycloid

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Dictionary.com

Dictionary.com is an online dictionary whose domain was first registered on May 14, 1995.

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Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

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Differential calculus

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Differential geometry of curves

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.

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Dimension of an algebraic variety

In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways.

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Diocles (mathematician)

Diocles (Διοκλῆς; c. 240 BC – c. 180 BC) was a Greek mathematician and geometer.

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Doubling the cube

Doubling the cube, also known as the Delian problem, is an ancient geometric problem.

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Dragon curve

A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.

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Elimination theory

In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.

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Elliptic curve

In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.

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Equivalence class

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

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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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Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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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 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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Fermat curve

In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation Therefore, in terms of the affine plane its equation is An integer solution to the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa.

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Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

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Gallery of curves

This is a gallery of curves, by Wikipedia page.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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General topology

In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.

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Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Hausdorff dimension

Hausdorff dimension is a measure of roughness in mathematics introduced in 1918 by mathematician Felix Hausdorff, and it serves as a measure of the local size of a space, taking into account the distance between its points.

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Helix

A helix, plural helixes or helices, is a type of smooth space curve, i.e. a curve in three-dimensional space.

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Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

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Homogeneous polynomial

In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.

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Implicit curve

In mathematics an implicit curve is a plane curve which is defined by an implicit equation relating the coordinate variables x and y. For example, the unit circle is defined by the implicit equation x^2+y^2.

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Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

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Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

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Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

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Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

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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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Koch snowflake

The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described.

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Lebesgue measure

In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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Linearity

Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.

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Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.

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List of curves

This is a list of curves, by Wikipedia page.

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List of curves topics

This is an alphabetical index of articles related to curves.

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List of geometers

A geometer is a mathematician whose area of study is geometry.

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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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Metric derivative

In mathematics, the metric derivative is a notion of derivative appropriate to parametrized paths in metric spaces.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Nicomedes (mathematician)

Nicomedes (Νικομήδης; c. 280 – c. 210 BC) was an ancient Greek mathematician.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Osculating circle

In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p. Its center lies on the inner normal line, and its curvature is the same as that of the given curve at that point.

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Parabola

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

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Parametric surface

A parametric surface is a surface in the Euclidean space \Bbb R^3 which is defined by a parametric equation with two parameters \vec r: \Bbb^2 \rightarrow \Bbb^3.

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Parametrization

Parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

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Path (topology)

In mathematics, a path in a topological space X is a continuous function f from the unit interval I.

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Peano curve

In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890.

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Perseus (geometer)

Perseus (Περσεύς; c. 150 BC) was an ancient Greek geometer, who invented the concept of spiric sections, in analogy to the conic sections studied by Apollonius of Perga.

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Phillips curve

The Phillips curve is a single-equation empirical model, named after William Phillips, describing a historical inverse relationship between rates of unemployment and corresponding rates of rises in wages that result within an economy.

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Piecewise

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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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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Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

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Projective geometry

Projective geometry is a topic in mathematics.

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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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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real algebraic geometry

In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings).

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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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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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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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Singular point of a curve

In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.

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Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

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Space-filling curve

In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an n-dimensional unit hypercube).

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Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Spiric section

In geometry, a spiric section, sometimes called a spiric of Perseus, is a quartic plane curve defined by equations of the form Equivalently, spiric sections can be defined as bicircular quartic curves that are symmetric with respect to the x and y-axes.

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Square

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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Squaring the circle

Squaring the circle is a problem proposed by ancient geometers.

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Tautochrone curve

A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point.

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Thomas Little Heath

Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer.

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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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Torus

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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Transcendental curve

In mathematics, a transcendental curve is a curve that is not an algebraic curve.

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Two-dimensional graph

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

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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).

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Vector-valued function

A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

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Winding number

In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point.

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World line

The world line (or worldline) of an object is the path that object traces in -dimensional spacetime.

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1-manifold, Closed curve, Continuous path, Curve (geometry), Curve (mathematics), Curved, Curved line, Curved lines, Differentiable curve, Mathematical curve, Mathematical curves, Mechanical curve, Open curve, Rectifiable path, Regular curve, Sharp curve, Simple curve, Skew curve, Space curve, Space curves.

References

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

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