| 释义 |
curve The graph of a continuous function y = f((x) defines a curve, or the variables x, y might be implicitly related as in x2 + xy + y2 = 1, which defines an ellipse, or a curve might be defined parametrically: x = cost, y = sint for 0 ≤ t<2π defines a circle. Classically, curves were defined by their geometry, but, with the introduction of Cartesian coordinates, they are easily defined by equations constraining the coordinates. Most generally, the term might refer to a 1-dimensional manifold, but it also refers to curves with singularities, such as y2 = x3, which has a cusp at the origin, or y2 = x2(x + 1), which has a node at the origin. If the variables x and y are complex numbers, then the Riemann surfaces defined may be referred to as curves, even though they have 2 real dimensions. See also Jordan curve, Peano curve.
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