# cardioid

A cardioid is a heart-shaped curve first studied in 1674 by the Danish astronomer Ole Römer who was trying to find the best shape for gear teeth. The curve appears to have been named by Giovanni Salvemini de Castillon (1708–1791).

When a circle rolls around another circle of the same size, any point on the moving circle traces out a cardioid. The Greeks used this fact when attempting to describe the motions of the planets. The cardioid is also the envelope of all circles with centers on a fixed circle, passing through one point on the fixed circle. In polar coordinates, it has the equation

*r* = 2*a *(1 - cos *θ*).

It can also be described as an epicycloid with one cusp.