List of curves explained

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 Leibnizhttps://web.archive.org/web/20041114002246/http://www.mathcurve.com/courbes2d/isochron/isochrone%20leibniz
  • Isochrone of Varignonhttps://web.archive.org/web/20041113201905/http://www.mathcurve.com/courbes2d/isochron/isochrone%20varignon
• Lamé curve
• Pursuit curve
• Rhumb line
• Sinusoid
• Spirals
  • Archimedean spiral
    • • Cornu spiral Cotes' spiral
      • Fermat's spiral Galileo's spiral http://www.mathcurve.com/courbes2d/galilee/galilee.shtml
        • • • • • 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 http://mathworld.wolfram.com/SeiffertsSphericalSpiral.html
• Slinky spiral http://mathworld.wolfram.com/Slinky.html
• 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

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
• An elementary treatise on cubic and quartic curves by Alfred Barnard Basset (1901) online at Google Books