A Novel Analysis of the Smooth Curve with Constant Width Based on a Time Delay System.

In this paper, we analyze the C ∞ smooth curve of constant width using the characteristic equation of a time delay system. We prove that a closed convex curve must be a circle if it is still a smooth curve of constant width after taking any number of derivatives. Finally, the simulation results are presented for analyzing the influence of derivative orders on a smooth non-circular curve of constant width. [ABSTRACT FROM AUTHOR]