# Euler's theorem

• For any element of $SO(3,\R)$, there is an axis such that that element can be viewed as rotation about that axis
• Every element of $SO(3,\R)$ is conjugate to an element of $SO(2,\R)$ (where $SO(2,\R)$ is embedded as $2 \times 2$-matrices)
• $SO(2,\R)$ is a conjugate-dense subgroup in $SO(3,\R)$