Math Tools Math Tools

Cardioid

An interactive cardioid — a heart-shaped curve traced by a point on a circle rolling around another circle of the same size. Drag the slider to rescale it. Looking for a different curve? Browse the full list of interactive curves.

Advertisement

Cardioid

Drag the slider to rescale the cardioid — it keeps its heart shape at any size.

Cardioid — The Details

A cardioid is a plane curve shaped like a heart (its name comes from the Greek word for heart, kardia), traced by a fixed point on the circumference of a circle as it rolls, without slipping, around the outside of a fixed circle of the same radius. It is a special case of both the limaçon and the epicycloid family — the case where the rolling circle and the fixed circle are exactly the same size. The same shape shows up as the caustic (reflected light pattern) cast by a circular light source onto the inside of a coffee cup, and cardioid-pattern microphones take their name from the same curve. With its cusp at the origin, it follows the polar equation:

$r = a(1 + \cos\theta)$

Advertisement