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The Spirograph


Introduction
Spirograph Tclet
The Mathematics
Variation I
Variation II
Gallery

Introduction

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.

The Mathematics

A simple derivation would yield,

Here, phi is a