Spirolateral

A figure formed by taking a series of steps of length 1, 2, ..., , with an angle $\theta$ turn after each step. The symbol for a spirolateral is ${}^{a_1, \ldots, a_k}n_\theta$ , where the s indicate that turns are in the $-\theta$ direction for these steps.

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_2_60.epsf scaled 500}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_3_36.epsf scaled 800}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_3_45.epsf scaled 800}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_3_72.epsf scaled 800}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_3_108.epsf scaled 800}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_90.epsf scaled 700}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{spirolateral_9_90_6.epsf scaled 700}\end{center}\end{figure}$

See also Maurer Rose, Spirograph

References

Gardner, M. ``Worm Paths.'' Ch. 17 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, 1986.

Odds, F. C. ``Spirolaterals.'' Math. Teacher 66, 121-124, 1973.