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)
editRational curves
editRational curves are subdivided according to the degree of the polynomial.
Degree 1
editDegree 2
editPlane curves of degree 2 are known as conics or conic sections and include
Degree 3
editCubic 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
editQuartic 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
- Limaçon
- Ovals of Cassini
- Squircle
- Three-leaved clover
Degree 5
editDegree 6
edit- Astroid
- Atriphtaloid
- Nephroid
- Quadrifolium
Curve families of variable degree
edit- Epicycloid
- Epispiral
- Epitrochoid
- Hypocycloid
- Hypotrochoid
- Lissajous curve
- Poinsot's spirals
- Rational normal curve
- Rose curve
Curves with genus 1
editCurves with genus > 1
edit- 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
edit- Polynomial lemniscate
- Fermat curve
- Sinusoidal spiral
- Superellipse
- Hurwitz surface
- Elkies trinomial curves
- Hyperelliptic curve
- Classical modular curve
- Cassini oval
Transcendental curves
edit- Bowditch curve
- Brachistochrone
- Butterfly curve (transcendental)
- Catenary
- Clélies
- Cochleoid
- Cycloid
- Horopter
- Isochrone
- Isochrone of Huygens (Tautochrone)
- Isochrone of Leibniz[1]
- Isochrone of Varignon[2]
- Lamé curve
- Pursuit curve
- Rhumb line
- Sinusoid
- Spirals
- Syntractrix
- Tractrix
- Trochoid
Piecewise constructions
editFractal curves
edit- 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
edit- 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]
- Slinky spiral [5]
- Space cardioid
- Twisted cubic
- Viviani's curve
Curves generated by other curves
edit- Caustic including Catacaustic and Diacaustic
- Cissoid
- Conchoid
- Evolute
- Glissette
- Inverse curve
- Involute
- Isoptic including Orthoptic
- Negative pedal curve
- Orthotomic
- Parallel curve
- Pedal curve
- Radial curve
- Roulette
- Strophoid
Applied Mathematics/Statistics/Physics/Engineering
editEconomics/Business
editMedicine/Biology
editPsychology
editEcology
editSee also
editExternal links
edit- 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