IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i4p557-d1337794.html
   My bibliography  Save this article

Geometry of Enumerable Class of Surfaces Associated with Mylar Balloons

Author

Listed:
  • Vladimir I. Pulov

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

  • Vasyl Kovalchuk

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

  • 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

In this paper, the very fundamental geometrical characteristics of the Mylar balloon like the profile curve, height, volume, arclength, surface area, crimping factor, etc. are recognized as geometrical moments I n ( x ) and I n and this observation has been used to introduce an infinite family of surfaces S n specified by the natural numbers n = 0 , 1 , 2 , … . These surfaces are presented via explicit formulas (through the incomplete Euler’s beta function) and can be identified as an interesting family of balloons. Their parameterizations is achieved relying on the well-known relationships among elliptic integrals, beta and gamma functions. The final results are expressed via the fundamental mathematical constants, such as π and the lemniscate constant ϖ . Quite interesting formulas for recursive calculations of various quantities related to associated figures modulo four are derived. The most principal results are summarized in a table, illustrated via a few graphics, and some direct relationships with other fundamental areas in mathematics, physics, and geometry are pointed out.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:557-:d:1337794
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/4/557/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/4/557/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:557-:d:1337794. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.