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
• 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

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)
  • [1]
  • [2]
• Lamé curve
• Pursuit curve
• Rhumb line
• Sinusoid
• Spirals
  • Archimedean spiral
  • Cornu spiral
  • Cotes' spiral
  • Fermat'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]
• [5]
• 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

Economics/Business[]

• Contract curve
• Cost curve
• Demand curve
  • Aggregate demand curve
  • Compensated demand curve
• Engel curve
• Hubbert curve
• Indifference curve
• J 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

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
• A Visual Directory 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