# List of curves

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.

## 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
* Conchoid of Dürer
* 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
* Three-leaved clover

##### Degree 6

* Astroid
* Atriphtaloid
* Nephroid
* Quadrifolium

##### Curve families of variable degree

* Epicycloid
* Epispiral
* Epitrochoid
* Hypocycloid
* Hypotrochoid
* 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
** Isochrone of Varignon
* Lamé curve
* Pursuit curve
* Rhumb line
* Sinusoid
* Spirals
** Archimedean spiral
** Cornu spiral
** Cotes' spiral
** Fermat's spiral
** Galileo's spiral
** 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
* Stadium
* 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
* Slinky spiral
* 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
* Duck 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 (biology)
* Oxygen–hemoglobin dissociation curve

## Psychology

* Forgetting curve
* Learning curve

## Ecology

* Species–area curve