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
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Zusammenfassung: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.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2007.11920452