This paper describes the math and technology required to project a variety of mathematical curves with a computerized laser light control system. The focus is upon creating “large-scale” animated laser projections of roulette or spirograph shapes, such as those found in the epitrochoid, hypotrochoid, epicycloid, and hypocycloid families. The projection process described utilizes a geometric approach that was first presented by the Greek or Egyptian mathematician and astronomer Ptolemy, that of “epicycles.” Examples of these laser images can be viewed at http://spot.colorado.edu/~lessley/.