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| {{short description|Type of planar curve with tree-like structure}} | {{short description|Type of planar curve with tree-like structure}} | ||
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| In ], particularly in ], a '''tree-like curve''' is a ] ] <math>c: S^1 \to \mathbb{R}^2</math> with the property that removing any ] splits the curve into exactly two ] ].<ref name="Shapiro-1997">Shapiro, B. (1997). "Tree-like curves and their number of inflection points". arXiv:dg-ga/9708009</ref> This property gives these curves a ]-like structure, hence their name. They were first systematically studied by ] ] ] and ] in the 1990s.<ref name="Shapiro-1997"/> | In ], particularly in ], a '''tree-like curve''' is a ] ] <math>c: S^1 \to \mathbb{R}^2</math> with the property that removing any ] splits the curve into exactly two ] ].<ref name="Shapiro-1997">Shapiro, B. (1997). "Tree-like curves and their number of inflection points". arXiv:dg-ga/9708009</ref> This property gives these curves a ]-like structure, hence their name. They were first systematically studied by ] ] ] and ] in the 1990s.<ref name="Shapiro-1997"/> | ||
Latest revision as of 07:15, 13 January 2025
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In mathematics, particularly in differential geometry, a tree-like curve is a generic immersion 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.
with the property that removing any References
See also
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