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Mylar Balloon and Associated Geometro-Mechanical Moments

Author

Listed:
  • Vasyl Kovalchuk

    (Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B, Pawińskiego Str., 02-106 Warsaw, Poland)

  • Vladimir I. Pulov

    (Department of Mathematics and Physics, Technical University of Varna, Studentska Str. 1, 9010 Varna, Bulgaria)

  • Ivaïlo M. Mladenov

    (Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria
    Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

Abstract

Starting with identifications of the very fundamental geometric characteristics of a Mylar balloon such as the profile curve, height, volume, arclength, surface area, crimping factor, etc., using the geometrical moments I n ( x ) and I n , we present explicit formulas for them and those of the mechanical moments of both solid and hollow balloons of arbitrary order. This is achieved by relying on the recursive relationships among elliptic integrals and the final results are expressed via the fundamental mathematical constants such as π , lemniscate constant ω ˜ , and Gauss’s constant G . An interesting periodicity modulo 4 was detected and accounted for in the final formulas for the moments. The principal results are illustrated by two tables, a few graphics, and some direct relationships with other fundamental areas in mathematics, physics and geometry are pointed out.

Suggested Citation

  • Vasyl Kovalchuk & Vladimir I. Pulov & Ivaïlo M. Mladenov, 2023. "Mylar Balloon and Associated Geometro-Mechanical Moments," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2646-:d:1167982
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    References listed on IDEAS

    as
    1. Peter H. Westfall, 2014. "Kurtosis as Peakedness, 1905-2014. R.I.P," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 191-195, April.
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    Cited by:

    1. Vladimir I. Pulov & Vasyl Kovalchuk & Ivaïlo M. Mladenov, 2024. "Geometry of Enumerable Class of Surfaces Associated with Mylar Balloons," Mathematics, MDPI, vol. 12(4), pages 1-18, February.

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