Crossword clues for evolute
evolute
The Collaborative International Dictionary
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.
Wiktionary
n. A curve comprising the center of curvature of another curve.
Wikipedia
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 R. For each point p in M and each vector v, based at p and normal to M, we associate the point . This defines a Lagrangian map, called the normal map. The caustic of the normal map is the evolute of M.
Usage examples of "evolute".
It dragged the yellow line of its orbit with it, opening the triangle into a four-sided evolute of ellipse.
The evolute stretched as Jupiter intersected the inner solar system, traced a sharp V around the Sun, and headed out into the depths of space again.
Era in effetti una croce e al centro c'era un uomo con le membra divaricate, ma un esame più attento le rivelò che su tutti e quattro i bracci della croce c'erano altri simboli che sembravano repliche deformi o evolute della figura centrale.
When finally they drew within hailing distance of each other they switched over to French and launched into an easy chat about involutes, evolutes, and radial curves.