List of curves

This is a list of curves, by Wikipedia page.

See also list of curve topics, list of surfaces, Riemann surface.

Algebraic curves

• Cubic plane curve
• Quartic plane curve
• Quintic plane curve
• Sextic plane curve

Rational curves

Degree 1

• Line

Degree 2

• Conic sections
  • Circle
  • Ellipse
  • Parabola
  • Hyperbola

Degree 3

• Folium of Descartes
• Cissoid of Diocles
• Conchoid of de Sluze
• Right strophoid
• Serpentine curve
• Trident curve
• Trisectrix of Maclaurin
• Tschirnhausen cubic
• Witch of Agnesi

Degree 4

• Ampersand curve
• Bean curve
• Bicorn
• Bow curve
• Bullet-nose curve
• Crooked egg curve
• Cruciform curve
• Deltoid curve
• Devil's curve
• Hippopede
• Kampyle of Eudoxus
• Kappa curve
• Lemniscate of Booth
• Lemniscate of Gerono
• Lemniscate of Bernoulli
• Limaçon
  • Cardioid
  • Limaçon trisectrix
• Trifolium curve

Degree 5

• Quintic of l'Hospital [1]

Degree 6

• Astroid
• Atriphtaloid
• Nephroid
• Quadrifolium

Families of variable degree

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

Curves of genus one

• Bicuspid curve
• Cassini oval
• Cassinoide
• Cubic curve
• Elliptic curve
• Watt's curve

Curves with genus greater than one

• Butterfly curve (algebraic)
• Elkies trinomial curves
• Hyperelliptic curve
• Klein quartic
• Classical modular curve
• Trott curve

Curve families with variable genus

• Polynomial lemniscate
• Fermat curve
• Sinusoidal spiral
• Superellipse

Transcendental curves

• Bowditch curve
• Brachistochrone
• Butterfly curve (transcendental)
• Catenary
• Clélies
• Cochleoid
• Curve of pursuit
• Cycloid
• Horopter
• Isochrone
  • Isochrone of Huygens (Tautochrone)
  • Isochrone of Leibniz[2]
  • Isochrone of Varignon[3]
• Lamé curve
• Rhumb line
• Spirals
  • Archimedean spiral
  • Cornu spiral
  • Cotes' spiral
  • Fermat's spiral
  • Galileo's spiral [4]
  • Hyperbolic spiral
  • Lituus
  • Logarithmic spiral
  • Nielsen's spiral
• Syntractrix
• Tractrix
• Trochoid

Piecewise constructions

• Bezier curve
• Splines
  • B-spline
  • Nonuniform rational B-spline
• Ogee
• Loess curve
• Lowess
• Polygonal curve
  • Maurer rose
• Reuleaux triangle

Fractal curves

• Blancmange curve
• De Rham curve
• Dragon curve
• Koch curve
• Lévy C curve
• space-filling curve, also known as the Peano curve
• Sierpinski curve

see also List of fractals by Hausdorff dimension

Curves in space

• Conchospiral
• Helix
• Seiffert's spiral [5]
• Slinky spiral [6]
• Twisted cubic
• Viviani's curve

Curves generated by other curves

• Caustic including Catacaustic and Diacaustic
• Cissoid
• Evolute
• Glissette
• Inverse curve
• Involute
• Isoptic including Orthoptic
• Orthotomic
• Negative pedal curve
• Pedal curve
• Roulette
• Strophoid

Named graphs

Economics

• Backward bending supply curve of labour
• Contract curve
• Cost curve
• Demand curve
  • Compensated demand curve
• Engel curve
• Indifference curve
• Laffer curve
• Lorenz curve
• Phillips curve
• J-curve

Other

• Bathtub curve
• Bell curve
• Calibration curve
• Cardiac function curve
• Dose-response curve
• Fletcher-Munson curve
• Forgetting curve
• Gompertz curve
• Growth curve
• Hubbert curve
• Kruithof curve
• Learning curve
• Light curve
• Logistic curve
• Oxyhemoglobin dissociation curve
• Paschen curve
• Robinson-Dadson curves
• Rotation curve
• Species-area curve
• Stress-strain curve

External links

• Famous Curves Index
• Two Dimensional Curves - has large pop-up advertisements
• 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