Evolute of a cycloid

The evolute of a cycloid. The blue cylcoid's [i]unit normal vector[/i] [b]N[/b] points toward its [i]center of curvature[/i], indicated by the red dot. The red dot traces all centers of curvature, which themselves form the red cycloid.
Evolute of a cycloid
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Information: Evolute of a cycloid