Math 2.0

Real functions Concept

Rectifiable curve

Builds on Parametrised curve

Summary

A parametrised curve is rectifiable when the lengths of the polygonal paths inscribed in it are bounded. The least upper bound of these lengths is the length of the curve.

Reading path

To understand this page from the ground up, read these 5 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 curveconceptRectifiable curve, concept, no evidence levelRectifiable 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. Rectifiable curve concept

Where this leads

5 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Arc_length, Definition
About this page
Tag0HATW2VWAZ
URIm2://0HATW2VWAZ
Aliasescurve-of-finite-length
Kindconcept
WritingW0 stub
MSC26A45
UsesParametrised curve

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