Plane curves: astroid, cardioid and abstract plane curve

What we do?
In this article we discuss how calculate the curvatures and moving frame.- As an example we calculate the curvatures and moving frame of the following plane curves: astroid, cardioid and abstract plane curve.
- We assume that astroid is given as a parametric curve in the Cartesian coordinate system and the cardioid is given as a parametric curve in the polar coordinate system.
- For abstract plane curve we will do the calculations in both systems.