Abstract
The halfturns generate the group H . What group of isometries does the set of reflections generate? Since a reflection is its own inverse, every element in this group must be a product of reflections (Theorem 2.4). A product of reflections is clearly an isometry; in this section we show that every isometry is a product of reflections. Thus, we shall see that the reflections generate all of H. The reflections are the building blocks for the symmetries of the plane.
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© 1982 Springer-Verlag New York Inc.
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Martin, G.E. (1982). Congruence. In: Transformation Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5680-9_5
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DOI: https://doi.org/10.1007/978-1-4612-5680-9_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5682-3
Online ISBN: 978-1-4612-5680-9
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