To Deduce the Polar from the Intrinsic Equation

Abstract

THE curve in which the radius of curvature is proportional to the arc is easily seen to be an equiangular spiral. if, as your correspondent assumes, the radius of curvature is inversely proportional to the arc, the problem is more complicated, and it is best in the first instance to express the Cartesian coordinates in terms of a third variable before attempting to form the polar equation. If instead of ps = c we write ps = frac12;k², we get with the usual notation