Math 2.0

concept

Rectifiable 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.

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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 node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Vector-valued function concept
  4. Parametrised curve concept
  5. Rectifiable curve concept

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2 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Arc_length, Definition

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Definitions