Gallery of curves

This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves.

Algebraic curves

Rational curves

Degree 1

• 
  Line

Degree 2

• 
  Circle
• 
  Ellipse
• 
  Parabola
• 
  Hyperbola

Degree 3

• 
  Cubic curve
• 
  Cubic polynomial
• 
  Folium of Descartes
• 
  Cissoid of Diocles
• 
  Conchoid of de Sluze
• 
  Cubic with double point
• 
  Strophoid
• 
  Semicubical parabola
• 
  Serpentine curve
• 
  Trident curve
• 
  Trisectrix of Maclaurin
• 
  Tschirnhausen cubic
• 
  Witch of Agnesi

Degree 4

• 
  Ampersand curve
• 
  Bean curve
• 
  Bicorn
• 
  Transformed bicorn
• 
  Bicuspid curve
• 
  Bow curve
• 
  Bullet-nose 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
• 
  Quadrifolium (2-rose)
• 
  Spiric sections
• 
  Squircle
• 
  Trifolium curve

Degree 5

Degree 6

• 
  Astroid
• 
  Atriphtaloid
• 
  Nephroid
• 
  Quadrifolium

Families of variable degree

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

Curves of genus one

• 
  Bicuspid curve
• 
  Cassini oval
• 
  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

Curve families with variable genus

• 
  Erdős lemniscate
• 
  Hurwitz surface
• 
  Mandelbrot curve
• 
  Polynomial lemniscate
• 
  Sinusoidal spiral
• 
  Superellipse

Transcendental curves

• 
  Bowditch curve
• 
  Brachistochrone
• 
  Butterfly curve (transcendental)
• 
  Catenary
• 
  Clélies
• 
  Cochleoid
• 
  Cycloid
• 
  Horopter
• 
  Isochrone
• 
  Pursuit curve
• 
  Rhumb line
• 
  Syntractrix
• 
  Tractrix
• 
  Trochoid

Spirals

• 
  Archimedean spiral
• 
  Cornu spiral
• 
  Fermat's spiral
• 
  Hyperbolic spiral
• 
  Lituus
• 
  Logarithmic spiral

Piecewise constructions

• 
  Maurer rose
• 
  Reuleaux triangle

Fractal curves

• 
  Blancmange curve
• 
  De Rham curve
• 
  Dragon curve
• 
  Koch curve
• 
  Lévy C curve
• 
  Peano curve
• 
  Sierpiński curve

External links

• Visual Dictionary of Special Plane Curves