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Evolute

In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center. Equivalently, an evolute is the envelope…

History, Properties of the evolute & Evolutes of some curves

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Overview

History

Evolute of a parametric curve

Properties of the evolute

Examples

Evolutes of some curves

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Evolute

Nodes46
Edges45
Triples71
Avg. degree1.96
Density0.043478
Components1

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Evolute

Top relations

related to References · 22
Evolute → Annales, Boris, Cordian, Curves, Edwards, EMS PressYates, Encyclopedia, Eric, Evolutes, Handbook, Institut Fourier, Mathematics, MathWorld, Piene, Plane Evolute, Ragni, Return, Riener, Shapiro, Sokolov
related to Properties of the evolute · 13
Evolute → At, For, Frenet, From, Hence, In, Kneser, See, Serret, Tait, That, The, This
related to Real algebraic properties and Singularities · 9
Evolute → Boris Shapiro, Cordian Riener, Evolutes, From, Lagrangian, Ragni Piene, The, These, They
related to history · 8
Evolute → Apollonius, BC, Book, Conics, However, Huygens, The, This
related to Evolute of log-aesthetic curves · 4
Evolute → Cesàro, Euler, One, The
related to Radial curve · 4
Evolute → For, The, Then, This
related to Evolute of a parametric curve · 3
Evolute → Big, For, If
related to Evolute of an implicit curve · 3
Evolute → At, For, Gamma
is a · 2
Evolute → envelope of the normals of the given curve.At sections of the curve with ρ, envelope of the normals to a curve.The evolute of a curve
related to Evolute of a cycloid · 1
Evolute → For

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Important terminology

curve displaystyle normal evolutes curvature vec rho point given frac curves vector center parabola cycloid one see map parametric properties

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Evoluteis aenvelope of the normals to a curve.The evolute of a curve0.90text
Evoluteis aenvelope of the normals of the given curve.At sections of the curve with ρ0.90text
cuspsinstance ofevolutes are envelopes of smooth families of lines and can exhibit typical singularities0.80text
Evoluterelated to Evolute of a cycloidFor0.60section
Evoluterelated to Evolute of a parametric curveIf0.60section
Evoluterelated to Evolute of a parametric curveFor0.60section
Evoluterelated to Evolute of a parametric curveBig0.60section
Evoluterelated to Evolute of an implicit curveFor0.60section
Evoluterelated to Evolute of an implicit curveGamma0.60section
Evoluterelated to Evolute of an implicit curveAt0.60section
Evoluterelated to Evolute of log-aesthetic curvesThe0.60section
Evoluterelated to Evolute of log-aesthetic curvesOne0.60section

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