Quadrature: Approximate Osculating Circles
- Author:
- Ryan Hirst
Before getting into the textbook, let me consider some ways that one might approximate the arc length of a curve.
Firstly, I can always use linear approximation: lay out points along the curve, draw straight lines between adjacent points, and add up the distances. But perhaps I can do better than this.
The lenght of the circular arc through three consecutive points on the curve responds to both first and second derivatives, and should be a much better approximation. Let me try it.