High Quality Content by WIKIPEDIA articles! In geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates r^n = a^n cos(n theta), where a is a nonzero constant and n is a rational number other than 0. With a rotation about the origin, this can also be written r^n = a^n sin(n theta)., The term spiral is a misnomer because they are not actually spirals and often have a flower-like shape. The inverse of a sinusoidal spiral with respect to a circle with center at the origin is another sinusoidal spiral whose value of n is the negative of the original curve's value of n. For example, the inverse of the lemniscate of Bernoulli is a hyperbola.

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