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This is an old revision of this page, as edited by GregariousMadness (talk | contribs) at 18:42, 12 January 2025 (←Created page with '{{short description|Type of planar curve with tree-like structure}} In mathematics, particularly in differential geometry, a '''tree-like curve''' is a generic immersion <math>c: S^1 \to \mathbb{R}^2</math> with the property that removing any double point splits the curve into exactly two disjoint connected components.<ref name="Shapiro-1997">Shapiro, B. (1997). "Tree-like curves and...'). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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

• Gauss diagram
• Inflection point

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