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.

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
 * 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
 * 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