Measurements and Transformations

Jürgen Richter-Gebert ()
Additional contact information
Jürgen Richter-Gebert: TU München, Zentrum Mathematik (M10) LS Geometrie

Chapter 21 in Perspectives on Projective Geometry, 2011, pp 399-422 from Springer

Abstract: 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.

Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-17286-1_21

Ordering information: This item can be ordered from
http://www.springer.com/9783642172861

DOI: 10.1007/978-3-642-17286-1_21

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().