[math] \newcommand{\mathds}{\mathbb}[/math]

This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.

Prove that the isometries of [math]\mathbb R^2[/math] are rotations or symmetries,

[[math]] R_t=\begin{pmatrix}\cos t&-\sin t\\ \sin t&\cos t\end{pmatrix}\quad,\quad S_t=\begin{pmatrix}\cos t&\sin t\\ \sin t&-\cos t\end{pmatrix} [[/math]]

and then try as well to find a formula for the isometries of [math]\mathbb R^3[/math].