ABSTRACT
We will discuss the shape of a curve in local terms, i.e., we will talk about the curve’s shape at a particular point x(t). In order to do this, it would be helpful to have a local coordinate system at x(t), thus enabling us to express local curve properties in terms of this system. We will base the construction of such a system on the first and second derivatives of the curve: x˙(t) and x¨(t), illustrated in Sketch 69.
