IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-88059-0_7.html
   My bibliography  Save this book chapter

Inducing the Symmetries Out of the Complexity: The Kepler Triangle and Its Kin as a Model Problem

In: Complex Symmetries

Author

Listed:
  • Takeshi Sugimoto

    (Kanagawa University, Faculty of Engineering)

Abstract

This essay is intended to exemplify how to solve a complex problem with several symmetries. The sample problem is a generalisation of the Kepler triangle. In 1597 Kepler discussed the golden-ratio related right-triangle, which is embedded in the cross-section of the Pharaoh Khufu’s pyramid. Three hundred years have passed since the first report, there are only three ‘such’ specimens known to mankind in the 21 Century. But the author broke through the solution space to reveal the three aspects: the golden ratio, the Fibonacci sequence and the Pythagorean Theorem. The path to the solution is explained from the starting point of collecting the data, by way of finding the invariants and to the goal of deriving the laws governing the solution space.

Suggested Citation

  • Takeshi Sugimoto, 2021. "Inducing the Symmetries Out of the Complexity: The Kepler Triangle and Its Kin as a Model Problem," Springer Books, in: György Darvas (ed.), Complex Symmetries, pages 71-78, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-88059-0_7
    DOI: 10.1007/978-3-030-88059-0_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-3-030-88059-0_7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.