Tree-like curve: Difference between revisions

Revision as of 18:42, 12 January 2025 editGregariousMadness (talk \| contribs)Extended confirmed users1,389 edits ←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...'Tag: Disambiguation links added		Revision as of 18:48, 12 January 2025 edit undoGregariousMadness (talk \| contribs)Extended confirmed users1,389 editsNo edit summaryNext edit →
Line 5:		Line 5:
	{{reflist}}		{{reflist}}
	==See also==		==See also==
			*]
	*]		*]
	*]		*]

Revision as of 18:48, 12 January 2025

Type of planar curve with tree-like structure

In mathematics, particularly in differential geometry, a tree-like curve is a generic immersion $c:S^{1}\to \mathbb {R} ^{2}$ 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.

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