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Vertices of Ovals with Constant Width Relative to Particular Circles

Author

Listed:
  • Adel Al-rabtah

    (Department of Mathematics and Statistics, Faculty of Science, Mutah University, Mutah, Al-Karak 61710, Jordan)

  • Kamal Al-Banawi

    (Department of Mathematics and Statistics, Faculty of Science, Mutah University, Mutah, Al-Karak 61710, Jordan)

Abstract

In this article, we study ovals of constant width in a plane, comparing them to particular circles. We use the vertices on the oval, after counting them, as a reference to measure the length of the curve between opposite points. A new proof of Barbier’s theorem is introduced. A distance function from the origin to the points of the oval is introduced, and it is shown that extreme values of the distance function occur at the vertices and opposite points. Comparisons are made between ovals and particular circles. We prove that the differences in the distances from the origin between the particular circles and the ovals are small and within a certain range. We also prove that all types of ovals described in this paper are analytically and geometrically enclosed between two defined circles centered at the origin.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4179-:d:1254369
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    References listed on IDEAS

    as
    1. 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.
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