Mathematica Packages for Plane Curves

Mathematica 7 notebook icon

Throughout this site you'll find downloadable Mathematica notebooks with this mma7 Mathematica icon icon. Mathematica is a technical computing system sold by Wolfram Research Inc. All artistic images and curve construction animations on this site are generated using Mathematica version 4 and the following packages.

As of 2009, Mathematica is at version 7. However, the packages here should work with Mathematica 7. (please write to me at if you find any problems.)

You can download MathPlayer to view images and animations in the following notebooks if you do not have Mathematica.

Mathematica Packages


ParaPlot does ParametricPlot with extended capabilities. All artistic images on this site are created by ParaPlot.


This package exports three category of functions:


This package exports about 30 functions that generate animations showing various ways to trace special plane curves. A typical function looks like EllipseGenerator[NumberOfFrames→30, LastFrameOnly→False] This package is designed to visually demonstrate various properties of special plane curves.


This package contain six graphics functions. TrochoidPlot, HypoTrochoidPlot, EpiTrochoidPlot, TrochoidGenerator, HypoTrochoidGenerator, and EpiTrochoidGenerator. The *Plot functions draw trochoid curves. The *Generator functions generates animation.

Some examples of graphics and movies generated by this package can be seen here: Epicycloid and Hypocycloid


This package define two graphic functions: MultiTrochoidPlot and TrochoidMovie. MultiTrochoidPlot plots multiple hypotrochoid and epitrochoids of various parameter settings, TrochoidMovie[] generates animations showing the effect of gradually varing one or more parameter on the curve generated. In other words, this package will draw SpiralGraphs and its mathematical variations.

Some examples of graphics and movies generated by this package can be seen here: Epicycloid and Hypocycloid.


Ruled surface are surfaces that can be generated by moving a line in space. This package exports several functions that plot ruled surfaces, including: RuledSurfacePlot[], CylinderPlot[], Oloid[], RegularTetrahedron[], Cube[], RightCircularCone[], HyperboloidOfOneSheet[], Helicoid[], HyperbolicParaboloid[]. The RuledSurfacePlot[] takes two space curves and connect them by lines to form a ruled surface.

Other Mathematica packages: