On a curve and a system

Curves of constant width, which have a very special place in many fields such as kinematics, engineering, art, cam design and geometry, are specially discussed under this title. In this study, a system of differential equations characterizing the curves of constant width is examined. This is the system of the first order homogenous differential equations with variable coefficients in the normal form. Approximate solutions of the system, by means of two different polynomial approaches, are calculated and error analysis is made. The obtained results are analyzed on a numerical sample and the best method of approach is determined. This system can also constitute a characterization for different types of curves according to different frames in different spaces. Therefore, this study is important not only for this curve type but also for the geometry of all curves that can be expressed in a similar system.