Introduction

Spirograph Tclet

The Mathematics

Variation I

Variation II

Gallery

Spirographs are beautiful patterns traced by a
pencil that is attached to a circle that rolls on the periphery of another
circle. In the figure shown below, P is the position of the pencil. The
green circle C1 has a radius R and the blue circle C2 has a radius r. P
is at a distance 'o' from the periphery of C2. We are interested in computing
the locus of P.

A simple derivation would yield,

x(theta) = R cos (theta) + (r+O) cos (phi)

y(theta) = R sin (theta) + (r+O) sin (phi)

Here, phi is a