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Annali di Matematica Pura ed Applicata

, Volume 53, Issue 1, pp 165–172 | Cite as

Similarities and conformal transformations

  • H. S. M. Coneter
Article

Summary

In ordinary Euclidean space, every isometry that leaves no point invariaut is either a screw displacement (including a translation as a special case) or a glide reflection. Every other kind of similarity is a spiral similarity: the product of a rotation about a line and a dilatation whose center lies on this line. In real inversive space (i.e., Euclidean space plus a single point at infinity), every conformal transformation is either a similarity or the product of an inversion and an isometry. This last remark remains valid when the number of dimensions is increased. In fact, every conformal transformation of inversive n-space (n/2) is expressible as the proddct of r reflections and s inversions, where r≤n+1, s≤2, r+s≤n+2.

Keywords

Euclidean Space Single Point Conformal Transformation Screw Displacement Spiral Similarity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Swets & Zeitlinger B. V. 1961

Authors and Affiliations

  • H. S. M. Coneter
    • 1
  1. 1.TorontoCanada

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