Evolute
![An ellipse (blue) and its evolute (green). The moving circle is the osculating circle to the ellipse, whose center is the center of curvature. It is also shown how the tangent line to the evolute is normal to the ellipse, i.e., the evolute is the envelope of the normals to the ellipse. The evolute of an ellipse is called an astroid.](/Images/godic/202502/05/Evolute_of_an_ellipse3855.gif")
![The evolute of a curve (in this case, an ellipse) is the envelope of its normals.](/Images/godic/202502/05/Evolute13856.gif")
![An ellipse (red), its evolute (blue) and some parallel curves. Note how the parallel curves touch the evolute where they have cusps](/Images/godic/202502/05/Evolute_and_parallel3856.gif")
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.