Annali di Matematica Pura ed Applicata

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

Similarities and conformal transformations

  • H. S. M. Coneter


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.


Euclidean Space Single Point Conformal Transformation Screw Displacement Spiral Similarity 
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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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