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

Author

Listed:
  • Teng Fu

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

  • Yusheng Zhou

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

Abstract

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.

Suggested Citation

  • Teng Fu & Yusheng Zhou, 2021. "A Novel Analysis of the Smooth Curve with Constant Width Based on a Time Delay System," Mathematics, MDPI, vol. 9(10), pages 1-7, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1131-:d:555884
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    Cited by:

    1. Adel Al-rabtah & Kamal Al-Banawi, 2023. "Vertices of Ovals with Constant Width Relative to Particular Circles," Mathematics, MDPI, vol. 11(19), pages 1-13, October.

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