As an example, we might minimize the integral (along the curve) of the square of the curvature, so thatf = (y",)2/(l + (y')2)512. However, the given data may come from physical measurements, where arbitrary units may be used for the physical quantities. If these points are plotted on a graph, the scales are usually chosen so that the set of points spans the available space oln the sheet. If we are dealing numerically with the set of numbers representing these data, this method of selecting a scale is inappropriate. The problem here is to find f(y, y', y") in (1) such that the smooth function y(x) remains unchanged with respect to the set of points { YJ} when these points are displaced or changed by a scale factor. That is, if y(x) is a smooth function associated with the data { Yi}, and if these data undergo a linear transformation Yi = aYi + b, the new solution y of (1) should be y = ay + b.