Cardioid

A plane algebraic curve of order four which is described by a point of a circle of radius rolling on a circle with the same radius ; an epicycloid with modulus . The equation of the cardioid in polar coordinates is:

In Cartesian coordinates it is:

The arc length from the cusp is:

The radius of curvature is:

The area bounded by the curve equals . The length of the curve is . The cardioid is a conchoid of the circle, a special case of a Pascal limaçon and a sinusoidal spiral.

Figure: c020390a

References

[1]	A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)

References

[a1]	J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)