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Double generating spirographic curves

Published online by Cambridge University Press:  03 February 2017

Stephan Berendonk
Stephan Berendonk*
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany e-mail: berendon@math.uni-bonn.de
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Extract

We can use a spirograph in different ways to draw curves. Do these different modes of drawing necessarily yield different curves, or is it also possible to get the same curve by using two different modes of drawing? We address this question geometrically, not using the parametric equations of the curves.

Type
Articles
Information
The Mathematical Gazette , Volume 101 , Issue 550 , March 2017 , pp. 27 - 37
Copyright
Copyright © Mathematical Association 2017 

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References

1. Cundy, H. M., Peritrochoids, Math. Gaz. 52 (May 1968) pp. 161–162.Google Scholar
2. Hall, L. M., Trochoids, roses, and thorns – beyond the spirograph, Coll. Math. J. 23 (1992) pp. 20–35.Google Scholar
3. Lockwood, E. H., A book of curves, Cambridge University Press (1961).Google Scholar