Closing curves by rearranging arcs

Leonardo Alese

Research output: Contribution to journalArticlepeer-review


We show how, under surprisingly weak assumptions, one can split a planar curve into three arcs and rearrange them (matching tangent directions) to obtain a closed curve. We also generalize this construction to curves split into k arcs and comment on what can be achieved by rearranging arcs for a curve in higher dimensions. Proofs involve only tools from elementary topology, and the paper is mostly self-contained.
Original languageEnglish
Pages (from-to)197-208
Number of pages12
JournalColloquium Mathematicum
Issue number2
Publication statusPublished - 2022


  • planar curve
  • rearrangement
  • topological method

ASJC Scopus subject areas

  • General Mathematics

Fields of Expertise

  • Information, Communication & Computing


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