Wolfram Demonstrations Project

Sinusoidal spirals are given by the equation

, where s is rational. They are not spirals; perhaps the name comes from the similar form of the equation for the logarithmic spiral,

. Change the values of s and a to see the various resulting curves, including hyperbolas, parabolas, cardioids, and lemniscates.

Contributed by: Rob Morris

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Sinusoidal Spirals