Concept information
Preferred term
four-vertex theorem
Definition(s)
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The four-vertex theorem of geometry states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima). The name of the theorem derives from the convention of calling an extreme point of the curvature function a vertex. This theorem has many generalizations, including a version for space curves where a vertex is defined as a point of vanishing torsion.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Four-vertex_theorem)
Broader concept(s)
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-T8G7FCDP-G
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