Propagation of curved folding: the folded annulus with multiple creases exists

Leonardo Alese

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)19-43
Number of pages25
JournalBeiträge zur Algebra und Geometrie
Issue number1
Publication statusPublished - Mar 2022


  • Circular pleat
  • Curved folding
  • Folded annulus
  • Origami

ASJC Scopus subject areas

  • Geometry and Topology
  • Algebra and Number Theory

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