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In mathematics, particularly in differential geometry, a tree-like curve is a generic immersion ${\displaystyle c:S^{1}\to \mathbb {R} ^{2}}$ with the property that removing any double point splits the curve into exactly two disjoint connected components. This property gives these curves a tree-like structure, hence their name. They were first systematically studied by Russian mathematicians Boris Shapiro and Vladimir Arnold in the 1990s.

References

1. ^ Shapiro, B. (1997). "Tree-like curves and their number of inflection points". arXiv:dg-ga/9708009

See also

• Arnold invariants
• Gauss diagram
• Inflection point

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