The rate of change of direction of a curve at a point on the curve. The Greek letter κ is used to denote curvature and
ρ= 1 κ is the radius of curvature which is the radius of the circle which best fits the curve at that point, matching the position, the gradient and the second differential of the curve at that point. The centre of curvature is the centre of that best-fitting circle, known as the circle of curvature.
If κ is positive, the centre will be above the curve and if κ is negative it will be below. Since is the radius of curvature, a curve which bends sharply at a point will have a small |ρ| and a correspondingly large value of |κ|.
Subjects: Mathematics — Astronomy and Astrophysics.