An alternative definition gives the curvature of a sufficiently differentiable plane curve to be |df/ds|, where ϕ is the angle between T and i (Figure 13.37a). Figure 13.37b shows the distance s measured

counterclockwise around the circle x² + y² = a² from the point (a, 0) to a point P, along with the angle ϕ at P. Calculate the circle’s curvature using the alternative definition.

Transcribed Image Text:

0 x² + y² = a² 0 پر a (a) T P TO S (b) T →X X s = 0 at (a,0) FIGURE 13.37 Figures for Exercise 31.