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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.

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.

- 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...

- roulette family of curves. The evolute of an involute is the original curve. The notions of the involute and evolute of a curve were introduced by Christiaan...

- \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...

- 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...

- 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...

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

- 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...

- dualism, the violation of physical conservation laws. Because mind is an evolute of matter, mental events are granted causal efficacy and are therefore...

- 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...

- 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...

- roulette family of curves. The evolute of an involute is the original curve. The notions of the involute and evolute of a curve were introduced by Christiaan...

- \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...

- 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...

- 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...

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

- 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...

- dualism, the violation of physical conservation laws. Because mind is an evolute of matter, mental events are granted causal efficacy and are therefore...

- 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...

- 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...

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