Abstract
Every isometry is a product of at most three reflections (Theorem 5.6). So each isometry is of the form σl, σmσl or σrσmσl. In this section the case σmσl is examined. Since a reflection is an involution, we know σlσl = l for any line l. Thus we are concerned with the product of two reflections in distinct lines l and m. There are two cases: either l and m are parallel or else l and m intersect at a unique point. We shall show first that if l and m are parallel lines then the product σmσl is the translation through twice the directed distance from l to m.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Martin, G.E. (1982). The Product of Two Reflections. In: Transformation Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5680-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5680-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5682-3
Online ISBN: 978-1-4612-5680-9
eBook Packages: Springer Book Archive