It's fairly well known that isometries in Euclidean space are composed of only translations, reflections and rotations. However, I'm finding it difficult to locate a proof of that. As usual, it's "intuitively obvious" but formally I'm not sure where to start.(adsbygoogle = window.adsbygoogle || []).push({});

Does anyone know of a good reference on geometry that might have one?

(My question is actually set in the context of reading about the Galilean group, with every element of that group being a composition of a rotation, translation and motion with uniform velocity. (Arnold's book on classical mechanics.))

Edit: There seems to be a uniqueness aspect to this too. It seems to me to be connected to the direct/semidirect product nature of the Euclidean group.

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# Decomposing Isometries

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