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evolutes
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Definitions of evolutes in various dictionaries:
noun - a type of geometric curve
EVOLUTES - 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 c...
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| Plural form of evolute. |
| a curve which is the locus of the centres of curvature of another curve (its involute). |
| A curve which is the locus of the centres of curvature of another curve (its involute). |
| Rolled outwards at the edges. |
| Evolutes description |
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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. * The evolute of a curve, a surface, or more generally a submanifold, is the caustic of the normal map. Let M be a smooth, regular submanifold in n. For each point p in M and each vector v, based at p and normal to M, we associate the point p + v. This defines a Lagrangian map, called the normal map. The caustic of the normal map is the evolute of M.Evolutes are closely connected to involutes: A curve is the evolute of any of its involutes. |