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Arc length

Arc length is the distance between two points along a curve. It can be formalized mathematically for smooth curves using vector calculus and differential geometry, or for curves that might not necessarily be smooth as a smallest upper bound of lengths of polygonal chains.

History, Historical methods & Finding arc lengths by integration

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Overview

Definition

Computation by an integral

Finding arc lengths by integration

Simple cases

Historical methods

Curves with infinite length

Generalization to (pseudo-)Riemannian manifolds

Sources

  • ISBN ISBN (identifier)

Advanced semantic analysis

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Map overview Semantic statistics

Arc length

Nodes105
Edges104
Triples52
Avg. degree1.98
Density0.019048
Components1

How this topic connects Entity context

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Arc length

Top relations

related to External links · 20
Arc length → Angela Sharp, Calculus Study Guide, Chad Pierson, CurvatureWeisstein, Curve Experiment Illustrates, Ed Pegg Jr, EMS Press, Encyclopedia, Eric, Famous Curves Index The, Josh Fritz, Length, Length Approximation, MacTutor History, Mathematics, MathWorld, Rectifiable, Rectification, The History, The Wolfram Demonstrations Project
related to Integral form · 9
Arc length → As, Before, De, Fermat, Geometric, Hendrik, Heuraet, In, Pierre
related to Computation by an integral · 7
Arc length → Euclidean, For, Here, More, The, This, Thus
related to Numerical integration · 7
Arc length → Because, But, For, In, Since, Taylor, The
related to Curve on a surface · 3
Arc length → Evaluating, Let, The
is a · 2
Arc length → distance between two points along a curve, smallest quantity that is not exceeded by the length of any polygonal path along the curve
related to Arcs of circles · 2
Arc length → Arc, Latin
related to Other simple cases · 2
Arc length → Arc, Archimedean

Important terminology Word statistics

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Important terminology

length curve arc displaystyle curves integral theta left right mathbf circle sqrt distance integrand frac vector lengths one coordinates sin

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Arc lengthis adistance between two points along a curve0.90text
Arc lengthis asmallest quantity that is not exceeded by the length of any polygonal path along the curve0.90text
Arc lengthrelated to Arcs of circlesArc0.60section
Arc lengthrelated to Arcs of circlesLatin0.60section
Arc lengthrelated to Computation by an integralFor0.60section
Arc lengthrelated to Computation by an integralThus0.60section
Arc lengthrelated to Computation by an integralEuclidean0.60section
Arc lengthrelated to Computation by an integralHere0.60section
Arc lengthrelated to Computation by an integralThis0.60section
Arc lengthrelated to Computation by an integralMore0.60section
Arc lengthrelated to Computation by an integralThe0.60section
Arc lengthrelated to Curve on a surfaceLet0.60section

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    Min side: 3
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