## Sinusoidal Spiral

A curve of the form

with Rational, which is not a true Spiral. Sinusoidal spirals were first studied by Maclaurin. Special cases are given in the following table.

 Curve Hyperbola Line Parabola Tschirnhausen Cubic 0 Logarithmic Spiral Cayley's Sextic Cardioid 1 Circle 2 Lemniscate

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 184, 1972.

Lee, X. Sinusoid.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/Sinusoid_dir/sinusoid.html.

Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 175, 1967.

MacTutor History of Mathematics Archive. Sinusoidal Spirals.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Sinusoidal.html.