The study of curves and their geometric properties is one of the oldest topics in mathematics. There are many interesting curves on a plane or sphere that are defined kinematically or geometrically and can be studied using the methods of calculus, differential equations, and differential geometry. For example, on a plane, one can mention tractrix, pursuit curve, lemniscate, brachistochrone, cycloid, conchoid of Nicomedes, limaçon of Pascal, etc., and on sphere great circle, spherical spiral, which is a special case of loxodrome also known as rhumb line, etc.