Measures of aberrancy.

Abstract

In much the same way that curvature provides a measure of the nonlinearity of a curve, aberrancy provides a measure of the noncircularity of a curve. Curvature can be defined in several ways, but they all result in the same formula. In contrast, different approaches to aberrancy yield different formulas. We consider a number of different approaches to aberrancy and show that there are some interesting and unexpected connections between them. This is a largely unexplored concept that can be used to generate projects for students in real analysis and calculus.