This paper describes the math and technology required to project a variety of mathematical curves with an innovative laser light control system. The focus is upon creating large-scale animated laser projections of spirograph shapes, such as those found among the epitrochoid, hypotrochoid, epicycloid, and hypocycloid curves. The process described utilizes an unusual math approach that was first presented by the Greek or Egyptian mathematician/astronomer Ptolemy. Instead of using the traditional spirograph techniques of rotating one wheel outside or inside of another wheel, the Laser Light Math system is structured around Ptolemy's idea of epicycles where one circle's center moves on the circumference of another circle. Traditional equations are modified to consider fully the elements of frequency, rotational direction, diameter, and offset.