List of curves

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This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, psychology, ecology, etc.

## Contents

* 1 Mathematics (Geometry)
* 1.1 Algebraic curves
* 1.1.1 Rational curves
* 1.1.1.1 Degree 1
* 1.1.1.2 Degree 2
* 1.1.1.3 Degree 3
* 1.1.1.4 Degree 4
* 1.1.1.5 Degree 5
* 1.1.1.6 Degree 6
* 1.1.1.7 Curve families of variable degree
* 1.1.2 Curves with genus 1
* 1.1.3 Curves with genus > 1
* 1.1.4 Curve families with variable genus
* 1.2 Transcendental curves
* 1.3 Piecewise constructions
* 1.4 Fractal curves
* 1.5 Space curves/Skew curves
* 1.6 Curves generated by other curves
* 2 Applied Mathematics/Statistics/Physics/Engineering
* 3 Economics/Business
* 4 Medicine/Biology
* 5 Psychology
* 6 Ecology
* 7 See also
* 8 External links

## Mathematics (Geometry)

### Algebraic curves

#### Rational curves

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

##### Degree 1

* Line

##### Degree 2

Plane curves of degree 2 are known as conics or conic sections and include

* Circle
* Unit circle
* Ellipse
* Parabola
* Hyperbola
* Unit hyperbola

##### Degree 3

Cubic plane curves include

* Cubic parabola
* Folium of Descartes
* Cissoid of Diocles
* Conchoid of de Sluze
* Right strophoid
* Semicubical parabola
* Serpentine curve
* Trident curve
* Trisectrix of Maclaurin
* Tschirnhausen cubic
* Witch of Agnesi

##### Degree 4

Quartic plane curves include

* Ampersand curve
* Bean curve
* Bicorn
* Bow curve
* Bullet-nose curve
* Cartesian oval
* Cruciform curve
* Deltoid curve
* Devil's curve
* Hippopede
* Kampyle of Eudoxus
* Kappa curve
* Lemniscate
* Lemniscate of Booth
* Lemniscate of Gerono
* Lemniscate of Bernoulli
* Limaçon
* Cardioid
* Limaçon trisectrix
* Ovals of Cassini
* Squircle
* Trifolium Curve

##### Degree 5

##### Degree 6

* Astroid
* Atriphtaloid
* Nephroid
* Quadrifolium

##### Curve families of variable degree

* Epicycloid
* Epispiral
* Epitrochoid
* Hypocycloid
* Lissajous curve
* Poinsot's spirals
* Rational normal curve
* Rose curve

#### Curves with genus 1

* Bicuspid curve
* Cassinoide
* Cubic curve
* Elliptic curve
* Watt's curve

#### Curves with genus > 1

* Bolza surface (genus 2)
* Klein quartic (genus 3)
* Bring's curve (genus 4)
* Macbeath surface (genus 7)
* Butterfly curve (algebraic) (genus 7)

#### Curve families with variable genus

* Polynomial lemniscate
* Fermat curve
* Sinusoidal spiral
* Superellipse
* Hurwitz surface
* Elkies trinomial curves
* Hyperelliptic curve
* Classical modular curve
* Cassini oval

### Transcendental curves

* Bowditch curve
* Brachistochrone
* Butterfly curve (transcendental)
* Catenary
* Clélies
* Cochleoid
* Cycloid
* Horopter
* Isochrone
* Isochrone of Huygens (Tautochrone)
* Isochrone of Leibniz[1]
* Isochrone of Varignon[2]
* Lamé curve
* Pursuit curve
* Rhumb line
* Sinusoid
* Spirals
* Archimedean spiral
* Cornu spiral
* Cotes' spiral
* Fermat's spiral
* Galileo's spiral [3]
* Hyperbolic spiral
* Lituus
* Logarithmic spiral
* Nielsen's spiral
* Syntractrix
* Tractrix
* Trochoid

### Piecewise constructions

* Bézier curve
* Loess curve
* Lowess
* Ogee
* Polygonal curve
* Maurer rose
* Reuleaux triangle
* Splines
* B-spline
* Nonuniform rational B-spline

### Fractal curves

* Blancmange curve
* De Rham curve
* Dragon curve
* Koch curve
* Lévy C curve
* Sierpiński curve
* Space-filling curve (Peano curve)

See also List of fractals by Hausdorff dimension.

### Space curves/Skew curves

* Conchospiral
* Helix
* Hemihelix, a quasi-helical shape characterized by multiple tendril perversions
* Tendril perversion (a transition between back-to-back helices)
* Seiffert's spiral [4]
* Slinky spiral [5]
* Space cardioid
* Twisted cubic
* Viviani's curve

### Curves generated by other curves

* Caustic including Catacaustic and Diacaustic
* Cissoid
* Conchoid
* Evolute
* Glissette
* Inverse curve
* Involute
* Isoptic including Orthoptic
* Negative pedal curve
* Fish curve
* Orthotomic
* Parallel curve
* Pedal curve
* Radial curve
* Roulette
* Strophoid

## Applied Mathematics/Statistics/Physics/Engineering

* Bathtub curve
* Bell curve
* Calibration curve
* Curve of growth (astronomy)
* Fletcher–Munson curve
* Galaxy rotation curve
* Gompertz curve
* Growth curve (statistics)
* Kruithof curve
* Light curve
* Logistic curve
* Paschen curve
* Robinson–Dadson curves
* Stress–strain curve
* Space-filling curve

## Economics/Business

* Contract curve
* Cost curve
* Demand curve
* Aggregate demand curve
* Compensated demand curve
* Engel curve
* Hubbert curve
* Indifference curve
* J curve
* Kuznets curve
* Laffer curve
* Lorenz curve
* Phillips curve
* Supply curve
* Aggregate supply curve
* Backward bending supply curve of labor

## Medicine/Biology

* Cardiac function curve
* Dose–response curve
* Growth curve
* Oxygen–hemoglobin dissociation curve

## Psychology

* Forgetting curve
* Learning curve

## Ecology

* Species–area curve

## See also

* Gallery of curves
* List of curves topics
* List of spirals
* List of surfaces
* Riemann surface
* Spherical curve

## External links

* Famous Curves Index
* Two Dimensional Curves
* Visual Dictionary of Special Plane Curves
* Curves and Surfaces Index (Harvey Mudd College)
* National Curve Bank
* "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

* v
* t
* e

Spirals, curves and helices

Curves|

* Algebraic
* Curvature
* Gallery
* List
* Topics

Helices|

* Angle
* Antenna
* Boerdijk–Coxeter
* Hemi
* Symmetry
* Triple

| Biochemistry|

* 310
* Alpha
* Beta
* Double
* Pi
* Polyproline
* Super
* Triple
* Collagen

|

Spirals|

* Archimedean
* Cotes's
* Epispiral
* Hyperbolic
* Poinsot's
* Euler
* Fermat's
* Golden
* Involute
* List
* Logarithmic
* On Spirals
* Theodorus

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