Cayley's sextic


In geometry, Cayley's sextic is a plane curve, a member of the sinusoidal spiral family, first discussed by Colin Maclaurin in 1718. Arthur Cayley was the first to study the curve in detail and it was named after him in 1900 by Raymond Clare Archibald.
The curve is symmetric about the x-axis and self-intersects at y = 0, x = −a/8. Other intercepts are at the origin, at and with the y-axis at ±a
The curve is the pedal curve of a cardioid with respect to its cusp.

Equations of the curve

The equation of the curve in polar coordinates is
In Cartesian coordinates the equation is
Cayley's sextic may be parametrised by the equations
The node is at t = ±π/3.