The documents listed below are Mathematica 3.0 notebooks. Clicking on the link below should cause your browser to download the document as a text file which can be opened by Mathematica 3.0/4.0 or MathReader 3.0/4.0. MathReader is a free program distributed by Wolfram Research that displays Mathematica documents.
Special Relativity and Curves in the Plane. A development of the basic Frenet frame theory in the Euclidean, Galilean, and Minkowskian planes with application to accelerated observers in special relativity. A revised version of this article appears in the March 2000 (vol. 107, no. 3) issue of The American Mathematical Monthly, pp.219—237. This notebook contains Mathemaitica code for the computations and figures in the Monthly article.
Curves with Periodic Curvature. Explores the fact that (omitting technicalities) a plane curve has a periodic cuvature function if and only if it is mapped into itself by a congruence of the plane. Curves with curvature specified as a function of distance from a line or a point are discussed (This includes both Newtonian and relativistic simple harmonic motion). Application: Any solution of y''=f(y) that crosses the axis three times is periodic.