IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i15p2348-d1707934.html
   My bibliography  Save this article

On the Number of Spherical Circles Needed to Cover a Spherical Convex Domain

Author

Listed:
  • Elad Atia

    (Computer Science Department, College of Management Academic Studies, Rishon LeZion 75490, Israel
    These authors contributed equally to this work.)

  • Reuven Cohen

    (Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
    These authors contributed equally to this work.)

  • Shai Gul

    (Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel
    These authors contributed equally to this work.)

Abstract

In this manuscript, we study the coverage of convex spherical domains by spherical circles. This question can be applied to the location of satellites, weather balloons, radio towers, etc. We present an upper bound on the number of spherical circles of radius r needed to cover a spherical convex domain K , in terms of the respective area and perimeter. Then, we calculate the asymptotic density of such cover, when the radius approaches zero.

Suggested Citation

  • Elad Atia & Reuven Cohen & Shai Gul, 2025. "On the Number of Spherical Circles Needed to Cover a Spherical Convex Domain," Mathematics, MDPI, vol. 13(15), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2348-:d:1707934
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/15/2348/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/15/2348/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:13:y:2025:i:15:p:2348-:d:1707934. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.