## Tangential Angle

For a Plane Curve, the tangential angle is defined by

 (1)

where is the Arc Length and is the Radius of Curvature. The tangential angle is therefore given by
 (2)

where is the Curvature. For a plane curve , the tangential angle can also be defined by
 (3)

Gray (1993) calls the Turning Angle instead of the tangential angle.

Gray, A. The Turning Angle.'' §1.6 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 13-14, 1993.