Euler's theorem

Statement
Euler's theorem is any of the following equivalent statements:


 * 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 $$SO(3,\R)$$