The Clothoid 

Introduction:The clothoid is interesting because its curvature varies linearly as the parameter t. It is one of the simplest examples of a curve that can be constructed from its curvature, although the math is somewhat complicated. There are also clothoids whose curvature varies as the n^{th} power of the parameter t. An example with n = 2 is plotted below. Note the extremely simple formula for arclength. Definition:, where The definition for a clothoid of degree n is too complicated to include here. Properties:
