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NCB Deposit #38

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A Collection of Famous Plane Curves
created in MATHEMATICA® by
Gustavo Gordillo
Möbius animation


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 a member of the faculty at Verdugo Hills High School, Verdugo Hills, CA.

  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

Gabriel's Horn
Möbius Strip

Upside-Down Shell


Necessary Packages Back

[Graphics:Images/index_gr_1.gif]

Astroid Back

Parametric[Graphics:Images/index_gr_2.gif]
Cartesian[Graphics:Images/index_gr_3.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_8.gif]
[Graphics:Images/index_gr_9.gif]
[Graphics:Images/index_gr_10.gif]

Cardiod Back

Cartesian[Graphics:Images/index_gr_11.gif]
Polar: [Graphics:Images/index_gr_12.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_17.gif]
[Graphics:Images/index_gr_18.gif]
[Graphics:Images/index_gr_19.gif]

Cassinian Ovals Back

Cartesian[Graphics:Images/index_gr_20.gif]
[Graphics:Images/index_gr_21.gif]
[Graphics:Images/index_gr_22.gif]

Catenary Back

Cartesian[Graphics:Images/index_gr_23.gif]
[Graphics:Images/index_gr_24.gif]
[Graphics:Images/index_gr_25.gif]

Cayley's Sextic Back

Cartesian[Graphics:Images/index_gr_26.gif]
Polar[Graphics:Images/index_gr_27.gif]
[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 Back

Parametric[Graphics:Images/index_gr_32.gif]
Cartesian[Graphics:Images/index_gr_33.gif]
Polar[Graphics:Images/index_gr_34.gif]
[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_39.gif]
[Graphics:Images/index_gr_40.gif]

Cissoid of Diocles Back

Cartesian[Graphics:Images/index_gr_41.gif]
Polar[Graphics:Images/index_gr_42.gif]
[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 Back

Polar[Graphics:Images/index_gr_47.gif]
[Graphics:Images/index_gr_48.gif]
[Graphics:Images/index_gr_49.gif]

Conchoid Back

Cartesian[Graphics:Images/index_gr_50.gif]
Polar[Graphics:Images/index_gr_51.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_56.gif]
Polar[Graphics:Images/index_gr_57.gif]
[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 Back

Parametric[Graphics:Images/index_gr_62.gif]
[Graphics:Images/index_gr_63.gif]
[Graphics:Images/index_gr_64.gif]

Devil's Curve Back

Cartesian[Graphics:Images/index_gr_65.gif]
Polar[Graphics:Images/index_gr_66.gif] (Special case)
[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 Back

Cartesian[Graphics:Images/index_gr_71.gif]
Polar[Graphics:Images/index_gr_72.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_77.gif]
[Graphics:Images/index_gr_78.gif]
[Graphics:Images/index_gr_79.gif]

Eight Curve Back

Cartesian[Graphics:Images/index_gr_80.gif]
Polar[Graphics:Images/index_gr_81.gif]
[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 Back

Parametrically[Graphics:Images/index_gr_86.gif]
Cartesian[Graphics:Images/index_gr_87.gif]
[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 Back

Parametric[Graphics:Images/index_gr_92.gif]
[Graphics:Images/index_gr_93.gif]
[Graphics:Images/index_gr_94.gif]

Epitrochoid Back

Parametric[Graphics:Images/index_gr_95.gif]
[Graphics:Images/index_gr_96.gif]
[Graphics:Images/index_gr_97.gif]

Equiangular Spiral Back

Polar[Graphics:Images/index_gr_98.gif]
[Graphics:Images/index_gr_99.gif]
[Graphics:Images/index_gr_100.gif]

Fermat's Spiral Back

Polar[Graphics:Images/index_gr_101.gif] θ
[Graphics:Images/index_gr_102.gif]
[Graphics:Images/index_gr_103.gif]

Folium Back

Cartesian[Graphics:Images/index_gr_104.gif]
Polar[Graphics:Images/index_gr_105.gif]
[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 Back

Parametrically[Graphics:Images/index_gr_110.gif]
Cartesian[Graphics:Images/index_gr_111.gif]
[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 Back

Polar[Graphics:Images/index_gr_116.gif]
[Graphics:Images/index_gr_117.gif]
[Graphics:Images/index_gr_118.gif]

Frequency Curve Back

Cartesian[Graphics:Images/index_gr_119.gif]
[Graphics:Images/index_gr_120.gif]
[Graphics:Images/index_gr_121.gif]

Hyperbola Back

Parametrically[Graphics:Images/index_gr_122.gif]
Cartesian[Graphics:Images/index_gr_123.gif]
[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 Back

Polar[Graphics:Images/index_gr_128.gif]
[Graphics:Images/index_gr_129.gif]
[Graphics:Images/index_gr_130.gif]

Hypocycloid Back

Parametric[Graphics:Images/index_gr_131.gif]
[Graphics:Images/index_gr_132.gif]
[Graphics:Images/index_gr_133.gif]

Hypotrochoid Back

Parametric[Graphics:Images/index_gr_134.gif]
[Graphics:Images/index_gr_135.gif]
[Graphics:Images/index_gr_136.gif]

Involute of a Circle Back

Parametric[Graphics:Images/index_gr_137.gif]
[Graphics:Images/index_gr_138.gif]
[Graphics:Images/index_gr_139.gif]

Kampyle of Eudoxus Back

Cartesian[Graphics:Images/index_gr_140.gif]
Polar[Graphics:Images/index_gr_141.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_146.gif]
Polar[Graphics:Images/index_gr_147.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_152.gif]
[Graphics:Images/index_gr_153.gif]
[Graphics:Images/index_gr_154.gif]

Lemniscate of Bernoulli Back

Cartesian[Graphics:Images/index_gr_155.gif]
Polar[Graphics:Images/index_gr_156.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_161.gif]
Polar[Graphics:Images/index_gr_162.gif]
[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 Back

Parametric[Graphics:Images/index_gr_167.gif]
[Graphics:Images/index_gr_168.gif]
[Graphics:Images/index_gr_169.gif]

Lituus Back

Polar[Graphics:Images/index_gr_170.gif]
[Graphics:Images/index_gr_171.gif]
[Graphics:Images/index_gr_172.gif]

Neile's Parabola Back

Cartesian[Graphics:Images/index_gr_173.gif]
[Graphics:Images/index_gr_174.gif]
[Graphics:Images/index_gr_175.gif]

Nephroid Back

Parametric[Graphics:Images/index_gr_176.gif]
[Graphics:Images/index_gr_177.gif]
[Graphics:Images/index_gr_178.gif]

Newton's Parabolas Back

Cartesian[Graphics:Images/index_gr_179.gif]
[Graphics:Images/index_gr_180.gif]
[Graphics:Images/index_gr_181.gif]

Parabola Back

Cartesian[Graphics:Images/index_gr_182.gif]
[Graphics:Images/index_gr_183.gif]
[Graphics:Images/index_gr_184.gif]

Pearls of de Sluze Back

Cartesian[Graphics:Images/index_gr_185.gif]
[Graphics:Images/index_gr_186.gif]
[Graphics:Images/index_gr_187.gif]

Pear-shaped Quartic Back

Cartesian[Graphics:Images/index_gr_188.gif]
[Graphics:Images/index_gr_189.gif]
[Graphics:Images/index_gr_190.gif]

Plateau Curves Back

Parametric[Graphics:Images/index_gr_191.gif]
[Graphics:Images/index_gr_192.gif]
[Graphics:Images/index_gr_193.gif]

Pursuit Curve Back

Cartesian[Graphics:Images/index_gr_194.gif]
[Graphics:Images/index_gr_195.gif]
[Graphics:Images/index_gr_196.gif]

Quadratrix of Hippias Back

Cartesian[Graphics:Images/index_gr_197.gif]
Polar[Graphics:Images/index_gr_198.gif]
[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 Back

Polar[Graphics:Images/index_gr_203.gif]
[Graphics:Images/index_gr_204.gif]
[Graphics:Images/index_gr_205.gif]

Right Strophoid Back

Cartesian[Graphics:Images/index_gr_206.gif]
Polar[Graphics:Images/index_gr_207.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_212.gif]
[Graphics:Images/index_gr_213.gif]
[Graphics:Images/index_gr_214.gif]

Sinusoidal Spirals Back

Polar[Graphics:Images/index_gr_215.gif]
[Graphics:Images/index_gr_216.gif]
[Graphics:Images/index_gr_217.gif]

Spiral of Archimedes Back

Polar[Graphics:Images/index_gr_218.gif]
[Graphics:Images/index_gr_219.gif]
[Graphics:Images/index_gr_220.gif]

Spiric Sections Back

Cartesian[Graphics:Images/index_gr_221.gif]
[Graphics:Images/index_gr_222.gif]
[Graphics:Images/index_gr_223.gif]

Straight Line Back

Cartesian[Graphics:Images/index_gr_224.gif]
Parametrically[Graphics:Images/index_gr_225.gif]
[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 Back

Parametric[Graphics:Images/index_gr_230.gif]
[Graphics:Images/index_gr_231.gif]
[Graphics:Images/index_gr_232.gif]

Tractrix Back

Parametric[Graphics:Images/index_gr_233.gif]
[Graphics:Images/index_gr_234.gif]
[Graphics:Images/index_gr_235.gif]

Tricuspoid Back

Parametrically[Graphics:Images/index_gr_236.gif]
Cartesian[Graphics:Images/index_gr_237.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_242.gif]
[Graphics:Images/index_gr_243.gif]
[Graphics:Images/index_gr_244.gif]

Trifolium Back

Cartesian[Graphics:Images/index_gr_245.gif]
Polar[Graphics:Images/index_gr_246.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_251.gif]
Polar[Graphics:Images/index_gr_252.gif]
[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 Back

Cartesian[Graphics:Images/index_gr_257.gif]
[Graphics:Images/index_gr_258.gif]
[Graphics:Images/index_gr_259.gif]

Watt's Curve Back

Polar[Graphics:Images/index_gr_260.gif]
[Graphics:Images/index_gr_261.gif]
[Graphics:Images/index_gr_262.gif]

Witch of Agnesi Back

Parametrically[Graphics:Images/index_gr_263.gif]
Cartesian[Graphics:Images/index_gr_264.gif]
[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 Back

To generate the animation in Mathematica, please type in the following commands.
[Graphics:Images/index_gr_269.gif]

Möbius Strip Back

To generate the animation in Mathematica, please type in the following commands.
[Graphics:Images/index_gr_270.gif]

Upside-Down Shell Back

To generate the animation in Mathematica, please type in the following commands.
[Graphics:Images/index_gr_271.gif]

Converted by Mathematica      August 14, 2001      Copyright © Gustavo Gordillo

Gus Gordillo gives special thanks to the Famous Curves Index at http://www-history.mcs.st-and.ac.uk/history/Curves/Curves.html

The National Curve Bank gives special thanks to Gus!

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