Abstract
This chapter gives a complete classification of isometries on a Euclidean plane, proves a technical theorem to be used later to develop the properties of dilations, and describes a method for constructing a translation with a given action.
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References
Bachmann, F.: Aufbau der Geometrie aus dem Spiegelungsbegriff, 2nd edn. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (1973). ISBN 978-3642655388
Behnke, H., Bachmann, F., Fladt, K., Kunle, H. (eds.): Fundamentals of Mathematics, vol. 2. MIT, Cambridge (1974). ISBN 978-0262020695. Chapter 3, Affine and Projective Planes, R. Lingenberg and A. Bauer; Chapter 4, Euclidean Planes, J. Diller and J. Boczec; also Chapter 5, Absolute Geometry, F. Bachmann, W. Pejas, H. Wolff, and A. Bauer; tr. by S. Gould
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© 2015 Springer International Publishing Switzerland
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Specht, E.J., Jones, H.T., Calkins, K.G., Rhoads, D.H. (2015). Isometries of a Euclidean Plane (ISM). In: Euclidean Geometry and its Subgeometries. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23775-6_12
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DOI: https://doi.org/10.1007/978-3-319-23775-6_12
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-23774-9
Online ISBN: 978-3-319-23775-6
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