Abstract
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 language | English |
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Pages (from-to) | 197-208 |
Number of pages | 12 |
Journal | Colloquium Mathematicum |
Volume | 169 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- planar curve
- rearrangement
- topological method
ASJC Scopus subject areas
- Mathematics(all)
Fields of Expertise
- Information, Communication & Computing