In geometry, a cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center of inversion. A cardioid can also be defined as the set of points of reflections of a fixed point on a circle through all tangents to the circle.
The caustic appearing on the surface of this cup of coffee is a cardioid.
Boundary of the central, period 1, region of the Mandelbrot set is a precise cardioid.
Cardioid formed by light on a watch dial.
In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve.
An ordinary cusp occurring as the caustic of light rays in the bottom of a teacup.