  In this paper we consider developable surfaces which are isometric to planar
domains and which are piecewise differentiable, exhibiting folds along curves.
The paper revolves around the longstanding problem of existence of the
so-called folded annulus with multiple creases, which we partially settle by
building upon a deeper understanding of how a curved fold propagates to
additional prescribed foldlines. After recalling some crucial properties of
developables, we describe the local behaviour of curved folding employing
normal curvature and relative torsion as parameters and then compute the very
general relation between such geometric descriptors at consecutive folds,
obtaining novel formulae enjoying a nice degree of symmetry. We make use of
these formulae to prove that any proper fold can be propagated to an arbitrary
finite number of rescaled copies of the first foldline and to give reasons why
problems involving infinitely many foldlines are harder to solve.
