In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arclength:
The total curvature of a closed curve is always an integer multiple of 2π, called the index of the curve, or turning number – it is the winding number of the unit tangent about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces.
Read more about Total Curvature: Comparison To Surfaces, Invariance, Generalizations
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“By sharing the information and observations with the caregiver, you have a chance to see your child through another pair of eyes. Because she has some distance and objectivity, a caregiver often sees things that a parent’s total involvement with her child doesn’t allow.”
—Amy Laura Dombro (20th century)