An Interesting Property of the Evolute

An Interesting Property of the Evolute

Escudero and Reventos discuss the property of the evolute. An evolute is the locus of centers of curvature of a plane curve. The evolute E of a smooth curve C has singularities. The cusps of the evolute correspond to the points of C where the curvature takes extreme values. In this equation, the evo...

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Veröffentlicht in:The American mathematical monthly 2007-08, Vol.114 (7), p.623-628
Hauptverfasser: Escudero, Carlos A., Reventós, Agustí
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Circles
Curvature
Geometric lines
Geometric planes
Geometry
Mathematical functions
Mathematical theorems
Property titles
Radius of curvature
Sine function
Theorems
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container_title The American mathematical monthly
container_volume 114
creator Escudero, Carlos A.
Reventós, Agustí
description Escudero and Reventos discuss the property of the evolute. An evolute is the locus of centers of curvature of a plane curve. The evolute E of a smooth curve C has singularities. The cusps of the evolute correspond to the points of C where the curvature takes extreme values. In this equation, the evolute of C is the envelope of all the normals to this curve.
doi_str_mv 10.1080/00029890.2007.11920452
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source Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection; JSTOR Mathematics & Statistics
subjects Algebra
Circles
Curvature
Geometric lines
Geometric planes
Geometry
Mathematical functions
Mathematical theorems
Property titles
Radius of curvature
Sine function
Theorems
title An Interesting Property of the Evolute
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