In the way of example, here is another wonder. Select 4 turns and draw tangents to the curve at the corresponding points. It must be noted that the curve through its point - equation is endowed with direction. The direction is naturally passed on to the tangent lines. Considering the lines as directed, there exists a unique cardioid tangent to the four lines whose direction agrees with the inherited direction of the lines.
Cardioid is traced by a point on a circle that rolls over a circle of the same radius.
The center of the stationary circle is said to be the center of the cardioid. Alexander Bogomolny 2790243 .