Curves, Envelopes, Evolutes
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in kinematics, e.g., as integral curves of vector fields, in other words as solutions of differential equations;
a variant: as envelopes of families of lines, or of families of other curves;
they also appear, in space, at the intersection of two surfaces (e.g., of a surface and a plane), therefore, they are useful for the study of surfaces (see Chapter VIII);
as the solutions of an algebraic equation P( x, y) = 0 (as conics in the plane, for instance), or of several algebraic equations (P1 (x, y, z) = P2 (x, y, z) = 0 in space(1) of dimension 3, etc.).
KeywordsSingular Point Parametrized Curve Plane Curve Curvature Center Perpendicular Bisector
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