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...

used), cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse. If the radius of the fixed circle is a then the equation...

of the circle k {\displaystyle k} , one gets a limaçon of Pascal. The evolute of a curve is the locus of centers of curvature. In detail: For a curve...

\varphi +\cos 3\varphi ,3\sin \varphi +\sin 3\varphi )} (see above). The evolute of a curve is the locus of centers of curvature. In detail: For a curve...

as the string is either unwrapped from or wrapped around the curve. The evolute of an involute is the original curve. It is generalized by the roulette...

An ellipse (red) and its evolute (blue). The dots are the vertices of the ellipse, at the points of greatest and least curvature....

curvature, form another curve, called the evolute of C. Vertices of C correspond to singular points on its evolute. Within any arc of a curve C within which...

typically only have 3-point contact with their osculating circle. The evolute of a curve will generically have a cusp when the curve has a vertex; other...

the curve and the envelope of such normals is its evolute. Therefore, YR is tangent to the evolute and the point Y is the foot of the perpendicular from...

(red) and its evolute (blue), the locus of its centers of curvature. The four marked vertices of the ellipse correspond to the four cusps of the evolute....