IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-17286-1_21.html
   My bibliography  Save this book chapter

Measurements and Transformations

In: Perspectives on Projective Geometry

Author

Listed:
  • Jürgen Richter-Gebert

    (TU München, Zentrum Mathematik (M10) LS Geometrie)

Abstract

While in the last chapter we have focused on measurement aspects and related analytic issues, we will return to more qualitative relations of objects in a Cayley-Klein geometry. In this and the next chapter we will mainly study the projective nature of Cayley-Klein geometries. This chapter focuses on aspects concerning transformations, their (projective) invariants, and the behavior of measurements under these transformations. The next chapter treats geometric objects and their elementary geometric properties, including some elementary geometric theorems. Although Cayley-Klein geometries unify several rather different types of geometric playgrounds in a common projective framework, each type of geometry (in the sense of Section 20.6) has its very special properties. This is due to the fact that the degeneracies of the fundamental conic of the geometry lead to degeneracies in the relevant geometric constructions. For this reason we will sometimes have to perform a special case analysis for the different types of Cayley-Klein geometries. Sometimes one general definition covers a certain effect (for instance reflection) in all types of geometries. Still it may be instructive to consider its particular specialization to certain geometries.

Suggested Citation

  • Jürgen Richter-Gebert, 2011. "Measurements and Transformations," Springer Books, in: Perspectives on Projective Geometry, chapter 21, pages 399-422, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-17286-1_21
    DOI: 10.1007/978-3-642-17286-1_21
    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

    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:978-3-642-17286-1_21. 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.