evolute
Sign in to savethumb|The blue parabola is the involute of the red curve. The red curve is the evolute of the blue parabola, and can be constructed as the locus of all centers of curvature of the blue parabola. right|thumb|The evolute of a curve (in this case, an ellipse) is the envelope of its normals.
Article
13 sectionsContents
- History
- Evolute of a parametric curve
- Evolute of an implicit curve
- Properties of the evolute
- Real algebraic properties and Singularities
- Examples
- Evolute of a parabola
- Evolute of an ellipse
- Evolute of a cycloid
- Evolute of log-aesthetic curves
- Evolutes of some curves
- Radial curve
- References
thumb|The blue parabola is the involute of the red curve. The red curve is the evolute of the blue parabola, and can be constructed as the locus of all centers of curvature of the blue parabola. right|thumb|The evolute of a curve (in this case, an ellipse) is the envelope of its normals.
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 of the normals to a curve.