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curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

s used in different fields:

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

(including

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...

, and

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...

engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...

medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

psychology Psychology is the science, scientific study of mind and behavior. Psychology includes the study of consciousness, conscious and Unconscious mind, unconscious phenomena, including feelings and thoughts. It is an academic discipline of immens ...

ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overl ...

, etc.

Mathematics (Geometry)

Algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane ...
s

Rational curves

Rational curves are subdivided according to the degree of the polynomial.

=Degree 1

= *

Line Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Art ...

=Degree 2

= Plane curves of degree 2 are known as conics or

conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a ...

s and include *

Circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...

Unit circle In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Eucli ...

Ellipse In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in ...

Parabola In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One descri ...

Hyperbola In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) 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. A hyperbola has two pieces, ca ...

Unit hyperbola In geometry, the unit hyperbola is the set of points (''x'',''y'') in the Cartesian plane that satisfy the implicit equation x^2 - y^2 = 1 . In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an ''alternative ra ...

=Degree 3

Cubic plane curve In mathematics, a cubic plane curve is a plane algebraic curve 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 ...

s include *

Cubic parabola In arithmetic and algebra, the cube of a number is its third power, that is, the result of multiplying three instances of together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example or . T ...

Folium of Descartes In geometry, the folium of Descartes (; named for René Decartes) is an algebraic curve defined by the implicit equation :x^3 + y^3 - 3 a x y = 0. History The curve was first proposed and studied by René Descartes in 1638. Its claim to fam ...

* Cissoid of Diocles * Conchoid of de Sluze *

Right strophoid In geometry, a strophoid is a curve generated from a given curve and points (the fixed point) and (the pole) as follows: Let be a variable line passing through and intersecting at . Now let and be the two points on whose distance from ...

Semicubical parabola In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form : y^2 - a^2 x^3 = 0 (with ) in some Cartesian coordinate system. Solving for leads to the ''explicit form'' : y = ...

Serpentine curve A serpentine curve is a curve whose equation is of the form :x^2y+a^2y-abx=0, \quad ab > 0. Equivalently, it has a parametric representation :x=a\cot(t), y=b\sin (t)\cos(t), or functional representation :y=\frac. The curve has an inflection po ...

Trident curve In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula: :xy+ax^3+bx^2+cx=d Trident curves are cubic plane curves with an ordinary double point in the real pro ...

Trisectrix of Maclaurin In algebraic geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. It can be defined as locus of the point of intersection of two lines, each rotating at a ...

Tschirnhausen cubic In algebraic geometry, the Tschirnhausen cubic, or Tschirnhaus' cubic is a plane curve defined, in its left-opening form, by the polar equation :r = a\sec^3 \left(\frac\right) where is the secant function. History The curve was studied by von ...

* Witch of Agnesi

=Degree 4

= Quartic plane curves include *

Ampersand curve In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: :Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0, with at least one o ...

Bean curve In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: :Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0, with at least one o ...

Bicorn In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation y^2 \left(a^2 - x^2\right) = \left(x^2 + 2ay - a^2\right)^2. It has two cusps and is symmetric about ...

Bow curve In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: :Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0, with at least one ...

Bullet-nose curve In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation :a^2y^2-b^2x^2=x^2y^2 \, The bullet curve has three double points in the real projective plane, at and , and , and and , and ...

Cartesian oval In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points ( foci). These curves are named after French mathematician René Descartes, who used them in optics. De ...

Cruciform curve In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: :Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0, with at least one o ...

* Deltoid curve *

Devil's curve In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form : y^2(y^2 - b^2) = x^2(x^2 - a^2). The polar equation of this curve is of the form :r = \sqrt = \sqrt. D ...

Hippopede In geometry, a hippopede () is a plane curve determined by an equation of the form :(x^2+y^2)^2=cx^2+dy^2, where it is assumed that and since the remaining cases either reduce to a single point or can be put into the given form with a rotatio ...

Kampyle of Eudoxus The Kampyle of Eudoxus (Greek: καμπύλη �ραμμή meaning simply "curved ine curve") is a curve with a Cartesian equation of :x^4 = a^2(x^2+y^2), from which the solution ''x'' = ''y'' = 0 is excluded. Alternative parameterizations In ...

Kappa curve In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter . The kappa curve was first studied by Gérard van Gutschoven around 1662. In the history of mathematics, it is remembered as one o ...

Lemniscate In algebraic geometry, a lemniscate is any of several figure-eight or -shaped curves. The word comes from the Latin "''lēmniscātus''" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "ribbons",. or which alternative ...

** Lemniscate of Booth **

Lemniscate of Gerono In algebraic geometry, the lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate In algebraic geometry, a lemniscate is any of several figure-eight o ...

Lemniscate of Bernoulli In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points and , known as foci, at distance from each other as the locus of points so that . The curve has a shape similar to the numeral 8 and to the ∞ symbol. ...

Limaçon In geometry, a limaçon or limacon , also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. I ...

Cardioid In geometry, a cardioid () is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal ...

Limaçon trisectrix In geometry, a limaçon trisectrix is the name for the quartic plane curve that is a trisectrix that is specified as a limaçon. The shape of the limaçon trisectrix can be specified by other curves particularly as a rose, conchoid or ep ...

Ovals of Cassini In geometry, a Cassini oval is a quartic plane curve defined as the locus (mathematics), locus of points in the plane (geometry), plane such that the Product_(mathematics), product of the distances to two fixed points (Focus (geometry), foci) is ...

Squircle A squircle is a shape intermediate between a square and a circle. There are at least two definitions of "squircle" in use, the most common of which is based on the superellipse. The word "squircle" is a portmanteau of the words "square" and "ci ...

* Trifolium Curve

=Degree 5

=Degree 6

= * Astroid *

Atriphtaloid An atriphtaloid, also called an atriphtothlassic curve, is type of sextic plane curve. It is given by the equation x^4 \left(x^2 + y^2\right) - \left(ax^2 - b\right)^2 = 0, where ''a'' and ''b'' are positive numbers. References

Sextic c ...

* Nephroid *

Quadrifolium The quadrifolium (also known as four-leaved clover) is a type of rose curve with an angular frequency of 2. It has the polar equation: :r = a\cos(2\theta), \, with corresponding algebraic equation :(x^2+y^2)^3 = a^2(x^2-y^2)^2. \, Rotated c ...

=Curve families of variable degree

= * Epicycloid *

Epispiral The epispiral is a plane curve with polar equation :\ r=a \sec. There are ''n'' sections if ''n'' is odd and 2''n'' if ''n'' is even. It is the polar or circle inversive geometry, inversion of the rose (mathematics), rose curve. In astronomy the ...

Epitrochoid In geometry, an epitrochoid ( or ) is a roulette traced by a point attached to a circle of radius rolling around the outside of a fixed circle of radius , where the point is at a distance from the center of the exterior circle. The parametric ...

Hypocycloid In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid cre ...

Lissajous curve A Lissajous curve , also known as Lissajous figure or Bowditch curve , is the graph of a system of parametric equations : x=A\sin(at+\delta),\quad y=B\sin(bt), which describe the superposition of two perpendicular oscillations in x and y dire ...

Poinsot's spirals In mathematics, Poinsot's spirals are two spirals represented by the polar equations : r = a\ \operatorname (n\theta) : r = a\ \operatorname (n\theta) where csch is the hyperbolic cosecant, and sech is the hyperbolic secant. They are named after ...

* Rational normal curve *

Rose curve A rose is either a woody perennial flowering plant of the genus ''Rosa'' (), in the family Rosaceae (), or the flower it bears. There are over three hundred Rose species, species and Garden roses, tens of thousands of cultivars. They form a ...

Curves with genus 1

Bicuspid curve In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: :Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0, with at least one o ...

Cassinoide In geometry, a Cassini oval is a quartic plane curve defined as the locus (mathematics), locus of points in the plane (geometry), plane such that the Product_(mathematics), product of the distances to two fixed points (Focus (geometry), foci) is ...

Cubic curve In mathematics, a cubic plane curve is a plane algebraic curve 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 eq ...

Elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. I ...

Watt's curve In mathematics, Watt's curve is a tricircular plane algebraic curve of degree six. It is generated by two circles of radius ''b'' with centers distance 2''a'' apart (taken to be at (±''a'', 0)). A line segment of length 2''c'' attaches to a ...

Curves with genus > 1

Bolza surface In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (introduced by ), is a compact Riemann surface of genus (mathematics), genus 2 with the highest possible order of the conformal map, conformal automorphism group in thi ...

(genus 2) *

Klein quartic In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus with the highest possible order automorphism group for this genus, namely order orientation-preserving automorphisms, and automorphisms ...

(genus 3) *

Bring's curve In mathematics, Bring's curve (also called Bring's surface) is the curve given by the equations :v+w+x+y+z=v^2+w^2+x^2+y^2+z^2=v^3+w^3+x^3+y^3+z^3=0. It was named by after Erland Samuel Bring who studied a similar construction in 1786 in a Promot ...

(genus 4) * Macbeath surface (genus 7) * Butterfly curve (algebraic) (genus 7)

Curve families with variable genus

Polynomial lemniscate In mathematics, a polynomial lemniscate or ''polynomial level curve'' is a plane algebraic curve of degree 2n, constructed from a polynomial ''p'' with complex coefficients of degree ''n''. For any such polynomial ''p'' and positive real number ' ...

* Fermat curve *

Sinusoidal spiral In algebraic geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates :r^n = a^n \cos(n \theta)\, where is a nonzero constant and is a rational number other than 0. With a rotation about the origin, ...

* Superellipse *

Hurwitz surface In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(''g'' − 1) automorphisms, where ''g'' is the genus of the surface. This number is maximal by virt ...

* Elkies trinomial curves *

Hyperelliptic curve In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus ''g'' > 1, given by an equation of the form y^2 + h(x)y = f(x) where ''f''(''x'') is a polynomial of degree ''n'' = 2''g'' + 1 > 4 or ''n'' = 2''g'' + 2 > 4 with ''n'' dis ...

* Classical modular curve *

Cassini oval In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points ( foci) is constant. This may be contrasted with an ellipse, for which the ''sum'' of t ...

Transcendental curves

* Bowditch curve * Brachistochrone * Butterfly curve (transcendental) *

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 in a uniform gravitational field. The catenary curve has a U-like shape, superfici ...

* Clélies *

Cochleoid In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation :r=\frac, the Cartesian equation :(x^2+y^2)\arctan\frac=ay, or the parametric equations :x=\frac, \quad y=\frac. The cochleo ...

Cycloid In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another cu ...

Horopter The horopter was originally defined in geometric terms as the locus of points in space that make the same angle at each eye with the fixation point, although more recently in studies of binocular vision it is taken to be the locus of points in spa ...

* Isochrone **''Isochrone of Huygens'' ( Tautochrone) ** Isochrone of Leibniz

** Isochrone of Varignon

*

Lamé curve A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape. In the C ...

Pursuit curve In geometry, a curve of pursuit is a curve constructed by analogy to having a point or points representing pursuers and pursuees; the curve of pursuit is the curve traced by the pursuers. With the paths of the pursuer and pursuee parameterize ...

Rhumb line In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north. Introduction The effect of following a rhumb l ...

Sinusoid A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...

Spiral In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:Archimedean spiral The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. It is the locus corresponding to the locations over time of a point moving away from a fixed point with a ...

Cornu spiral An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals. Eu ...

Cotes' spiral Introduction In physics and in the mathematics of plane curves, a Cotes's spiral (also written Cotes' spiral and Cotes spiral) is one of a family of spirals classified by Roger Cotes. Cotes introduces his analysis of these curves as follows: “ ...

Fermat's spiral A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant. As a result, the distance between turns grows in inverse proportion to their distance ...

Galileo's spiral Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

br>
**

Hyperbolic spiral A hyperbolic spiral is a plane curve, which can be described in polar coordinates by the equation :r=\frac of a hyperbola In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in ...

Lituus The word ''lituus'' originally meant a curved augural staff, or a curved war-trumpet in the ancient Latin language. This Latin word continued in use through the 18th century as an alternative to the vernacular names of various musical instruments ...

Logarithmic spiral A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). More ...

Nielsen's spiral In mathematics, trigonometric integrals are a indexed family, family of integrals involving trigonometric functions. Sine integral The different sine integral definitions are \operatorname(x) = \int_0^x\frac\,dt \operatorname(x) = -\int ...

Syntractrix A syntractrix is a curve of the form :x+\sqrt= a \ln \frac. It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve.Dionysius Lardner Prof ...

Tractrix In geometry, a tractrix (; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the ''tractor'') that moves at a right ...

Trochoid In geometry, a trochoid () is a roulette curve formed by a circle rolling along a line. It is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line. If the ...

Piecewise constructions

Bézier curve A Bézier curve ( ) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape ...

* Loess curve *

Lowess Local regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally es ...

Ogee An ogee ( ) is the name given to objects, elements, and curves—often seen in architecture and building trades—that have been variously described as serpentine-, extended S-, or sigmoid-shaped. Ogees consist of a "double curve", the combinat ...

* Polygonal curve **

Maurer rose In geometry, the concept of a Maurer rose was introduced by Peter M. Maurer in his article titled ''A Rose is a Rose... A Maurer rose consists of some lines that connect some points on a rose curve. Definition Let ''r'' = sin(''nθ'') ...

Reuleaux triangle A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circular disks, each having its center on the boundary of the ...

* Splines **

B-spline In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expresse ...

** Nonuniform rational B-spline

Fractal curves

Blancmange curve In mathematics, the blancmange curve is a self-affine curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi who described it in 1901, or as the Takagi–Landsberg curve, a generalization of the cur ...

De Rham curve In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham. The Cantor function, Cesàro curve, Minkowski's question mark function, the Lévy C curve, the blancmange curve, and Koch curve are all spe ...

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. The dragon curve is probably most commonly thought of as the shape that is generated from rep ...

Koch curve The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curv ...

* Lévy C curve * Sierpiński curve *

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). Because Giuseppe Peano (1858–1932) was the first to discover one, ...

(''Peano curve'') See also

List of fractals by Hausdorff dimension According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illus ...

Space curves/Skew curves

* Conchospiral *

Helix A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helic ...

** Hemihelix, a quasi-helical shape characterized by multiple tendril perversions **

Tendril perversion Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed. Such a reversal of chirality is commonly seen in helical plant tendril ...

(a transition between back-to-back helices) *

Seiffert's spiral Seiffert's spherical spiral is a curve on a sphere made by moving on the sphere with constant speed and angular velocity with respect to a fixed diameter. If the selected diameter is the line from the north pole to the south pole, then the requir ...

br>
* Slinky spiralbr>
* Twisted cubic *

Viviani's curve In mathematics, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani. It is the intersection of a sphere with a cylinder that is tangent to the sphere and ...

Curves generated by other curves

Caustic Caustic most commonly refers to: * Causticity, a property of various corrosive substances ** Sodium hydroxide, sometimes called ''caustic soda'' ** Potassium hydroxide, sometimes called ''caustic potash'' ** Calcium oxide, sometimes called ''caust ...

including Catacaustic and Diacaustic *

Cissoid In geometry, a cissoid (() is a plane curve generated from two given curves , and a point (the pole). Let be a variable line passing through and intersecting at and at . Let be the point on so that \overline = \overline. (There are actua ...

* Conchoid *

Evolute In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that cur ...

Glissette In geometry, a glissette is a curve determined by either the locus of any point, or the envelope of any line or curve, that is attached to a curve that slides against or along two other fixed curves. Examples Ellipse A basic example is that of a ...

Inverse curve In inversive geometry, an inverse curve of a given curve is the result of applying an inverse operation to . Specifically, with respect to a fixed circle with center and radius the inverse of a point is the point for which lies on the ray ...

Involute In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from o ...

Isoptic In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle. Examples: # The orthoptic of a parabola is its directrix (proof: see below), # The orthoptic of an ellipse \tfrac + \ ...

including Orthoptic *

Negative pedal curve In geometry, a negative pedal curve is a plane curve that can be constructed from another plane curve ''C'' and a fixed point ''P'' on that curve. For each point ''X'' ≠ ''P'' on the curve ''C'', the negative pedal curve has a tange ...

Fish curve A fish curve is an ellipse negative pedal curve that is shaped like a fish. In a fish curve, the pedal point is at the focus for the special case of the squared eccentricity e^2=\tfrac. The parametric equations for a fish curve correspond to th ...

* Orthotomic *

Parallel curve A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of '' parallel (straight) lines''. It can also be defined as a curve whose points are at a constant ''normal distance'' f ...

Pedal curve A pedal (from the Latin '' pes'' ''pedis'', "foot") is a lever designed to be operated by foot and may refer to: Computers and other equipment * Footmouse, a foot-operated computer mouse * In medical transcription, a pedal is used to control ...

* Radial curve *

Roulette Roulette is a casino game named after the French word meaning ''little wheel'' which was likely developed from the Italian game Biribi''.'' In the game, a player may choose to place a bet on a single number, various groupings of numbers, the ...

Strophoid In geometry, a strophoid is a curve generated from a given curve and points (the fixed point) and (the pole) as follows: Let be a variable line passing through and intersecting at . Now let and be the two points on whose distance from ...

Applied Mathematics/Statistics/Physics/Engineering

Bathtub curve The bathtub curve is widely used in reliability engineering and deterioration modeling. It describes a particular form of the hazard function which comprises three parts: *The first part is a decreasing failure rate, known as early failures. *Th ...

* Bell curve * Calibration curve *

Curve of growth In astronomy, the curve of growth describes the equivalent width of a spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow freque ...

(astronomy) *

Fletcher–Munson curve An equal-loudness contour is a measure of sound pressure level, over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon and i ...

* Galaxy rotation curve *

Gompertz curve The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. Th ...

Growth curve (statistics) The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as seen in the definition. Definition Growth c ...

* Kruithof curve *

Light curve In astronomy, a light curve is a graph of light intensity of a celestial object or region as a function of time, typically with the magnitude of light received on the y axis and with time on the x axis. The light is usually in a particular frequ ...

Logistic curve A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the ...

* Paschen curve *

Robinson–Dadson curves The Robinson–Dadson curves are one of many sets of equal-loudness contours for the human ear, determined experimentally by D. W. Robinson and R. S. Dadson. Until recently, it was common to see the term 'Fletcher–Munson curves, Fletcher–Muns ...

Stress–strain curve In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress ...

Economics/Business

* Contract curve *

Cost curve In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible ...

Demand curve In economics, a demand curve is a graph depicting the relationship between the price of a certain commodity (the ''y''-axis) and the quantity of that commodity that is demanded at that price (the ''x''-axis). Demand curves can be used either for ...

Aggregate demand curve In macroeconomics, aggregate demand (AD) or domestic final demand (DFD) is the total demand for final goods and services in an economy at a given time. It is often called effective demand, though at other times this term is distinguished. This is ...

** Compensated demand curve * Engel curve *

Hubbert curve The Hubbert curve is an approximation of the production rate of a resource over time. It is a symmetric logistic distribution curve, often confused with the "normal" gaussian function. It first appeared in "Nuclear Energy and the Fossil Fuels ...

Indifference curve In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is ''indifferent''. That is, any combinations of two products indicated by the curve will provide the c ...

J curve A J curve is any of a variety of J-shaped diagrams where a curve initially falls, then steeply rises above the starting point. Political economy Balance of trade model In economics, the "J curve" is the time path of a country’s trade balan ...

Kuznets curve The Kuznets curve () expresses a hypothesis advanced by economist Simon Kuznets in the 1950s and 1960s. According to this hypothesis, as an economy develops, market forces first increase and then decrease economic inequality. The Kuznets curve ...

Laffer curve In economics, the Laffer curve illustrates a theoretical relationship between rates of taxation and the resulting levels of the government's tax revenue. The Laffer curve assumes that no tax revenue is raised at the extreme tax rates of 0% and ...

Lorenz curve In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution. The curve is a graph showing the prop ...

Phillips curve The Phillips curve is an economic model, named after William Phillips hypothesizing a correlation between reduction in unemployment and increased rates of wage rises within an economy. While Phillips himself did not state a linked relationship ...

Supply curve In economics, supply is the amount of a resource that firms, producers, labourers, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual. Supply can be in produced goods, l ...

Aggregate supply curve In economics, aggregate supply (AS) or domestic final supply (DFS) is the total supply of goods and services that firms in a national economy plan on selling during a specific time period. It is the total amount of goods and services that firms ...

Backward bending supply curve of labor In economics, a backward-bending supply curve of labour, or backward-bending labour supply curve, is a graphical device showing a situation in which as real (inflation-corrected) wages increase beyond a certain level, people will substitute time p ...

Medicine/Biology

Cardiac function curve A cardiac function curve is a graph showing the relationship between right atrial pressure (x-axis) and cardiac output (y-axis).Superimposition of the cardiac function curve and venous return curve is used in one hemodynamic model. __TOC__ Shape ...

* Dose–response curve *

Growth curve (biology) A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size or biomass (in population ecology and demography, for population growth analysis), i ...

Oxygen–hemoglobin dissociation curve The oxygen–hemoglobin dissociation curve, also called the oxyhemoglobin dissociation curve or oxygen dissociation curve (ODC), is a curve that plots the proportion of hemoglobin in its saturated ( oxygen-laden) form on the vertical axis agains ...

Psychology

* Forgetting curve *

Learning curve A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Proficiency (measured on the vertical axis) usually increases with increased experience (the ...

Ecology

* Species–area curve

External links

Famous Curves IndexTwo Dimensional Curves"Courbes 2D" at Encyclopédie des Formes Mathématiques Remarquables"Courbes 3D" at Encyclopédie des Formes Mathématiques Remarquables
*''An elementary treatise on cubic and quartic curves'' by Alfred Barnard Basset (1901
online at Google Books
{{DEFAULTSORT:Curves * * Lists of shapes