Sinusoidal spiral
![Sinusoidal spirals: equilateral hyperbola (n = -2), line (n = -1), parabola (n = -1/2), cardioid (n = 1/2), circle (n = 1) and lemniscate of Bernoulli (n = 2), where rn = 1n cos(nθ) in polar coordinates and their equivalents in rectangular coordinates.](/Images/godic/202502/11/Sinusoidal_spirals.svg2521.png")
In geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates
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
The term "spiral" is a misnomer, because they are not actually spirals, and often have a flower-like shape. Many well known curves are sinusoidal spirals including: