# Definition of Evolute. Meaning of Evolute. Synonyms of Evolute

Here you will find one or more explanations in English for the word Evolute. Also in the bottom left of the page several parts of wikipedia pages related to the word Evolute and, of course, Evolute synonyms and on the right images related to the word Evolute.

## Definition of Evolute

Evolute
Evolute Ev"o*lute, n. [L. evolutus unrolled, p. p. of evolvere. See Evolve.] (Geom.) A curve from which another curve, called the involute or evolvent, is described by the end of a thread gradually wound upon the former, or unwound from it. See Involute. It is the locus of the centers of all the circles which are osculatory to the given curve or evolvent. Note: Any curve may be an evolute, the term being applied to it only in its relation to the involute.

## Meaning of Evolute from wikipedia

- 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...
- 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...
- 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...
- \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...
- (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....
- Mamikon's theorem. The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a cosh ⁠x/a⁠...