# Bridges 2012 Short Paper

Projecting Mathematical Curves with Laser Light

Merrill Lessley and Paul Beale

(Proceedings pages 557–560)

## Abstract

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.

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