National Curve Bank

Famous Curves

Famous Curves

This collection of 62 famous curves, with equations and code, was created by Gustavo Gordillo for the NCB when he was an undergraduate. He used Mathematica 4.0 for Students. Gus is now an instructor at California State University, Los Angeles.

Curve, Equation and Code Index

Necessary Packages	Fermat's Spiral	Pearls of de Sluze
Astroid	Folium	Pear-shaped Quartic
Bicorn	Folium of Descartes	Plateau Curves
Cardiod	Freeth's Nephroid	Pursuit Curve
Cartesian Oval	Frequency Curve	Quadratrix of Hippias
Catenary	Hyperbola	Rhodonea Curves
Cayley's Sextic	Hyperbolic Spiral	Right Strophoid
Circle	Hypocycloid	Serpentine
Cissoid of Diocles	Hypotrochoid	Sinusoidal Spirals
Cochleoid	Involute of a Circle	Spiral of Archimedes
Conchoid	Kampyle of Eudoxus	Spiric Sections
Conchoid of de Sluze	Kappa Curve	Straight Line
Cycloid	Lamé Curves	Talbot's Curve
Devil's Curve	Lemniscate of Bernoulli	Tractrix
Double Folium	Limacon of Pascal	Tricuspoid
Dürer's Shell Curves	Lissajous Curves	Trident of Newton
Eight Curve	Lituus	Trifolium
Ellipse	Neile's Parabola	Trisectrix of Maclaurin
Epicycloid	Nephroid	Tschirnhaus' Cubic
Epitrochoid	Newton's Parabolas	Watt's Curve
Equiangular Spiral	Parabola	Witch of Agnesi

Animation Index

Upside-Down Shell

Necessary Packages

[Graphics:Images/index_gr_1.gif]

Astroid

Parametric

Cartesian:

[Graphics:Images/index_gr_4.gif]

[Graphics:Images/index_gr_5.gif]

[Graphics:Images/index_gr_6.gif]

[Graphics:Images/index_gr_7.gif]

Bicorn

Cartesian:

[Graphics:Images/index_gr_9.gif]

[Graphics:Images/index_gr_10.gif]

Cardiod

Cartesian:

Polar:

[Graphics:Images/index_gr_13.gif]

[Graphics:Images/index_gr_14.gif]

[Graphics:Images/index_gr_15.gif]

[Graphics:Images/index_gr_16.gif]

Cartesian Oval

Cartesian:

[Graphics:Images/index_gr_18.gif]

[Graphics:Images/index_gr_19.gif]

Cassinian Ovals

Cartesian:

[Graphics:Images/index_gr_21.gif]

[Graphics:Images/index_gr_22.gif]

Catenary

Cartesian:

[Graphics:Images/index_gr_24.gif]

[Graphics:Images/index_gr_25.gif]

Cayley's Sextic

Cartesian:

Polar:

[Graphics:Images/index_gr_28.gif]

[Graphics:Images/index_gr_29.gif]

[Graphics:Images/index_gr_30.gif]

[Graphics:Images/index_gr_31.gif]

Circle

Parametric:

Cartesian:

Polar:

[Graphics:Images/index_gr_35.gif]

[Graphics:Images/index_gr_36.gif]

[Graphics:Images/index_gr_37.gif]

[Graphics:Images/index_gr_38.gif]

[Graphics:Images/index_gr_40.gif]

Cissoid of Diocles

Cartesian:

Polar:

[Graphics:Images/index_gr_43.gif]

[Graphics:Images/index_gr_44.gif]

[Graphics:Images/index_gr_45.gif]

[Graphics:Images/index_gr_46.gif]

Cochleoid

Polar:

[Graphics:Images/index_gr_48.gif]

[Graphics:Images/index_gr_49.gif]

Conchoid

Cartesian:

Polar:

[Graphics:Images/index_gr_52.gif]

[Graphics:Images/index_gr_53.gif]

[Graphics:Images/index_gr_54.gif]

[Graphics:Images/index_gr_55.gif]

Conchoid of de Sluze

Cartesian:

Polar:

[Graphics:Images/index_gr_58.gif]

[Graphics:Images/index_gr_59.gif]

[Graphics:Images/index_gr_60.gif]

[Graphics:Images/index_gr_61.gif]

Cycloid

Parametric:

[Graphics:Images/index_gr_63.gif]

[Graphics:Images/index_gr_64.gif]

Devil's Curve

Cartesian:

Polar: [Graphics:Images/index_gr_66.gif]

(Special case)
[Graphics:Images/index_gr_67.gif]

[Graphics:Images/index_gr_67.gif]

[Graphics:Images/index_gr_68.gif]

[Graphics:Images/index_gr_69.gif]

[Graphics:Images/index_gr_70.gif]

Double Folium

Cartesian:

Polar:

[Graphics:Images/index_gr_73.gif]

[Graphics:Images/index_gr_74.gif]

[Graphics:Images/index_gr_75.gif]

[Graphics:Images/index_gr_76.gif]

Dürer's Shell Curves

Cartesian:

[Graphics:Images/index_gr_78.gif]

[Graphics:Images/index_gr_79.gif]

Eight Curve

Cartesian:

Polar:

[Graphics:Images/index_gr_82.gif]

[Graphics:Images/index_gr_83.gif]

[Graphics:Images/index_gr_84.gif]

[Graphics:Images/index_gr_85.gif]

Ellipse

Parametrically:

Cartesian:

[Graphics:Images/index_gr_88.gif]

[Graphics:Images/index_gr_89.gif]

[Graphics:Images/index_gr_90.gif]

[Graphics:Images/index_gr_91.gif]

Epicycloid

Parametric:

[Graphics:Images/index_gr_93.gif]

[Graphics:Images/index_gr_94.gif]

Epitrochoid

Parametric:

[Graphics:Images/index_gr_96.gif]

[Graphics:Images/index_gr_97.gif]

Equiangular Spiral

Polar:

[Graphics:Images/index_gr_99.gif]

[Graphics:Images/index_gr_100.gif]

Fermat's Spiral

Polar:

θ

[Graphics:Images/index_gr_103.gif]

Folium

Cartesian:

Polar:

[Graphics:Images/index_gr_106.gif]

[Graphics:Images/index_gr_107.gif]

[Graphics:Images/index_gr_108.gif]

[Graphics:Images/index_gr_109.gif]

Folium of Descartes

Parametrically:

Cartesian:

[Graphics:Images/index_gr_112.gif]

[Graphics:Images/index_gr_113.gif]

[Graphics:Images/index_gr_114.gif]

[Graphics:Images/index_gr_115.gif]

Freeth's Nephroid

Polar:

[Graphics:Images/index_gr_117.gif]

[Graphics:Images/index_gr_118.gif]

Frequency Curve

Cartesian:

[Graphics:Images/index_gr_120.gif]

[Graphics:Images/index_gr_121.gif]

Hyperbola

Parametrically:

Cartesian:

[Graphics:Images/index_gr_124.gif]

[Graphics:Images/index_gr_125.gif]

[Graphics:Images/index_gr_126.gif]

[Graphics:Images/index_gr_127.gif]

Hyperbolic Spiral

Polar:

[Graphics:Images/index_gr_129.gif]

[Graphics:Images/index_gr_130.gif]

Hypocycloid

Parametric:

[Graphics:Images/index_gr_132.gif]

[Graphics:Images/index_gr_133.gif]

Hypotrochoid

Parametric:

[Graphics:Images/index_gr_135.gif]

[Graphics:Images/index_gr_136.gif]

Involute of a Circle

Parametric:

[Graphics:Images/index_gr_138.gif]

[Graphics:Images/index_gr_139.gif]

Kampyle of Eudoxus

Cartesian:

Polar:

[Graphics:Images/index_gr_142.gif]

[Graphics:Images/index_gr_143.gif]

[Graphics:Images/index_gr_144.gif]

[Graphics:Images/index_gr_145.gif]

Kappa Curve

Cartesian:

Polar:

[Graphics:Images/index_gr_148.gif]

[Graphics:Images/index_gr_149.gif]

[Graphics:Images/index_gr_150.gif]

[Graphics:Images/index_gr_151.gif]

Lamé Curves

Cartesian:

[Graphics:Images/index_gr_153.gif]

[Graphics:Images/index_gr_154.gif]

Lemniscate of Bernoulli

Cartesian:

Polar:

[Graphics:Images/index_gr_157.gif]

[Graphics:Images/index_gr_158.gif]

[Graphics:Images/index_gr_159.gif]

[Graphics:Images/index_gr_160.gif]

Limacon of Pascal

Cartesian:

Polar:

[Graphics:Images/index_gr_163.gif]

[Graphics:Images/index_gr_164.gif]

[Graphics:Images/index_gr_165.gif]

[Graphics:Images/index_gr_166.gif]

Lissajous Curves

Parametric:

[Graphics:Images/index_gr_168.gif]

[Graphics:Images/index_gr_169.gif]

Lituus

Polar:

[Graphics:Images/index_gr_171.gif]

[Graphics:Images/index_gr_172.gif]

Neile's Parabola

Cartesian:

[Graphics:Images/index_gr_174.gif]

[Graphics:Images/index_gr_175.gif]

Nephroid

Parametric:

[Graphics:Images/index_gr_177.gif]

[Graphics:Images/index_gr_178.gif]

Newton's Parabolas

Cartesian:

[Graphics:Images/index_gr_180.gif]

[Graphics:Images/index_gr_181.gif]

Parabola

Cartesian:

[Graphics:Images/index_gr_183.gif]

[Graphics:Images/index_gr_184.gif]

Pearls of de Sluze

Cartesian:

[Graphics:Images/index_gr_186.gif]

[Graphics:Images/index_gr_187.gif]

Pear-shaped Quartic

Cartesian:

[Graphics:Images/index_gr_189.gif]

[Graphics:Images/index_gr_190.gif]

Plateau Curves

Parametric:

[Graphics:Images/index_gr_192.gif]

[Graphics:Images/index_gr_193.gif]

Pursuit Curve

Cartesian:

[Graphics:Images/index_gr_196.gif]

Quadratrix of Hippias

Cartesian:

Polar:

[Graphics:Images/index_gr_199.gif]

[Graphics:Images/index_gr_200.gif]

[Graphics:Images/index_gr_201.gif]

[Graphics:Images/index_gr_202.gif]

Rhodonea Curves

Polar:

[Graphics:Images/index_gr_204.gif]

[Graphics:Images/index_gr_205.gif]

Right Strophoid

Cartesian:

Polar:

[Graphics:Images/index_gr_208.gif]

[Graphics:Images/index_gr_209.gif]

[Graphics:Images/index_gr_210.gif]

[Graphics:Images/index_gr_211.gif]

Serpentine

Cartesian:

[Graphics:Images/index_gr_213.gif]

[Graphics:Images/index_gr_214.gif]

Sinusoidal Spirals

Polar:

[Graphics:Images/index_gr_216.gif]

[Graphics:Images/index_gr_217.gif]

Spiral of Archimedes

Polar:

[Graphics:Images/index_gr_219.gif]

[Graphics:Images/index_gr_220.gif]

Spiric Sections

Cartesian:

[Graphics:Images/index_gr_222.gif]

[Graphics:Images/index_gr_223.gif]

Straight Line

Cartesian:

Parametrically:

[Graphics:Images/index_gr_226.gif]

[Graphics:Images/index_gr_227.gif]

[Graphics:Images/index_gr_228.gif]

[Graphics:Images/index_gr_229.gif]

Talbot's Curve

Parametric:

[Graphics:Images/index_gr_231.gif]

[Graphics:Images/index_gr_232.gif]

Tractrix

Parametric:

[Graphics:Images/index_gr_234.gif]

[Graphics:Images/index_gr_235.gif]

Tricuspoid

Parametrically:

Cartesian:

[Graphics:Images/index_gr_238.gif]

[Graphics:Images/index_gr_239.gif]

[Graphics:Images/index_gr_240.gif]

[Graphics:Images/index_gr_241.gif]

Trident of Newton

Cartesian:

[Graphics:Images/index_gr_243.gif]

[Graphics:Images/index_gr_244.gif]

Trifolium

Cartesian:

Polar:

[Graphics:Images/index_gr_247.gif]

[Graphics:Images/index_gr_248.gif]

[Graphics:Images/index_gr_249.gif]

[Graphics:Images/index_gr_250.gif]

Trisectrix of Maclaurin

Cartesian:

Polar:

[Graphics:Images/index_gr_253.gif]

[Graphics:Images/index_gr_254.gif]

[Graphics:Images/index_gr_255.gif]

[Graphics:Images/index_gr_256.gif]

Tschirnhaus' Cubic

Cartesian:

[Graphics:Images/index_gr_258.gif]

[Graphics:Images/index_gr_259.gif]

Watt's Curve

Polar:

[Graphics:Images/index_gr_261.gif]

[Graphics:Images/index_gr_262.gif]

Witch of Agnesi

Parametrically:

Cartesian:

[Graphics:Images/index_gr_265.gif]

[Graphics:Images/index_gr_266.gif]

[Graphics:Images/index_gr_267.gif]

[Graphics:Images/index_gr_268.gif]

Gabriel's Horn

To generate the animation in Mathematica, please type in the following commands.

[Graphics:Images/index_gr_269.gif]

Möbius Strip

To generate the animation in Mathematica, please type in the following commands.

[Graphics:Images/index_gr_270.gif]

Upside-Down Shell

To generate the animation in Mathematica, please type in the following commands.

[Graphics:Images/index_gr_271.gif]