Sinusoidal spiral
Family of curves of the form r^n = a^n cos(nθ) / From Wikipedia, the free encyclopedia
In algebraic 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:
- Rectangular hyperbola (n = −2)
- Line (n = −1)
- Parabola (n = −1/2)
- Tschirnhausen cubic (n = −1/3)
- Cayley's sextet (n = 1/3)
- Cardioid (n = 1/2)
- Circle (n = 1)
- Lemniscate of Bernoulli (n = 2)
The curves were first studied by Colin Maclaurin.