list of curves
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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 curve]]s=
==Rational curves==
Rational curves are subdivided according to the degree of the polynomial.
===Degree 1===
===Degree 2===
Plane curves of degree 2 are known as conics or conic sections and include
===Degree 3===
===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 5===
===Degree 6===
- Astroid
- Atriphtaloid
- Nephroid
- Quadrifolium
===Curve families of variable degree===
==Curves with genus 1==
==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==
=Transcendental curves=
- Bowditch curve
- Brachistochrone
- Butterfly curve (transcendental)
- Catenary
- Clélies
- Cochleoid
- Cycloid
- Horopter
- Isochrone
- Isochrone of Huygens (Tautochrone)
- Isochrone of Leibniz[https://web.archive.org/web/20041114002246/http://www.mathcurve.com/courbes2d/isochron/isochrone%20leibniz]
- Isochrone of Varignon[https://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=
=Fractal curves=
=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
Economics/Business
Medicine/Biology
Psychology
Ecology
See also
External links
- [https://mathshistory.st-andrews.ac.uk/Curves/ Famous Curves Index]
- [http://www.2dcurves.com/ Two Dimensional Curves]
- [http://xahlee.info/SpecialPlaneCurves_dir/specialPlaneCurves.html Visual Dictionary of Special Plane Curves]
- [https://web.archive.org/web/20110606113358/http://www.math.hmc.edu/~gu/math142/mellon/curves_and_surfaces/all.html Curves and Surfaces Index (Harvey Mudd College)]
- [https://web.archive.org/web/20021011081334/http://curvebank.calstatela.edu/home/home.htm National Curve Bank]
- An elementary treatise on cubic and quartic curves by Alfred Barnard Basset (1901) [https://books.google.com/books?id=yUxtAAAAMAAJ&q=Circular+cubic online at Google Books]
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