Math 2.0

Differential geometry Concept

Regular curve

Builds on Parametrised curveTangent vector of a curve

Summary

A regular curve is a continuously differentiable parametrised curve whose tangent vector is never zero. At each point a regular curve has a well-defined tangent line, and it can be reparametrised by arc length.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptVector-valued function, concept, no evidence levelVector-valued functionconceptParametrised curve, concept, no evidence levelParametrised curveconceptTangent vector of a curve, concept, no evidence levelTangent vector of a c…conceptRegular curve, concept, no evidence levelRegular curveconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Vector-valued function concept
  4. Parametrised curve concept
  5. Tangent vector of a curve concept
  6. Regular curve concept

Where this leads

1 page builds on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Differentiable_curve, Definitions
About this page
Tag0V7090SSPC
URIm2://0V7090SSPC
Aliasesregular-parametrised-curve
Kindconcept
WritingW0 stub
MSC53A04
SpecializesParametrised curve
UsesParametrised curve, Tangent vector of a curve

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