If a smooth curve C has velocity v and normal acceleration at a point P, then R (the radius of curvature of curve C at P) =

Proof

By Proposition 3 

In view of Proposition 8, there are the steps of construction:

Figure 4 The radius of curvature

1. Construct v and a.

2. Project a to the line ( which goes through O and is  perpendicular to v ) at A'.

3. Construct a line perpendicular to at v and intersect at V'.

4. Construct the image O' of the point P translated by the vector .