Misplaced Pages

Revision as of 07:15, 13 January 2025

This article relies largely or entirely on a single source. Please help improve this article by introducing citations to additional sources. Find sources: "Tree-like curve" – news · newspapers · books · scholar · JSTOR (January 2025)

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

This geometry-related article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e

• Differential geometry
• Curves
• Geometry stubs