  We show that the relations which define the algebras of the quantum Euclidean
planes $\b{R}^N_q$ can be expressed in terms of projections provided that the
unique central element, the radial distance from the origin, is fixed. The
resulting reduced algebras without center are the quantum Euclidean spheres
$S^{N-1}_q$. The projections $e=e^2=e^*$ are elements in
$\Mat_{2^n}(S^{N-1}_q)$, with N=2n+1 or N=2n, and can be regarded as defining
modules of sections of q-generalizations of monopoles, instantons or more
general twisted bundles over the spheres. We also give the algebraic definition
of normal and cotangent bundles over the spheres in terms of canonically
defined projections in $\Mat_{N}(S^{N-1}_q)$.
