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esolutes
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There are 8 letters in ESOLUTES ( E1L1O1S1T1U1 )
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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 ℝn. 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. |