Curve - ορισμός. Τι είναι το Curve
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Τι (ποιος) είναι Curve - ορισμός

MATHEMATICAL IDEALIZATION OF THE TRACE LEFT BY A MOVING POINT
Jordan curve; Continuous path; Closed curve; Space curve; Curved; Arc (geometry); Skew curve; Mathematical curves; Mechanical curve; Major arc; Arc (curvature); Regular curve; ◠; ◡; ◜; ◝; ◞; ◟; 1-manifold; Smooth curve; Simple curve; Open curve; Mathematical curve; Space curves; Curve (geometry); Great arc; Sharp curve; Arc shaped; Curve (mathematics); ⌒; Arc (geometric); Curved line; Curve segment; Curved line segment; Curved lines; Great-circle arc; Continuous curve; Subarc; Path (geometry); Topological curve; Surface curve; Curve (topology)
  • The curves created by slicing a cone ([[conic section]]s) were among the curves studied in ancient [[Greek mathematics]].
  • Analytic geometry allowed curves, such as the [[Folium of Descartes]], to be defined using equations instead of geometrical construction.
  • A [[dragon curve]] with a positive area
  • [[Megalithic art]] from Newgrange showing an early interest in curves
  • A [[parabola]], one of the simplest curves, after (straight) lines

Curve         
·adj Bent without angles; crooked; curved; as, a curve line; a curve surface.
II. Curve ·vi To bend or turn gradually from a given direction; as, the road curves to the right.
III. Curve ·adj A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.
IV. Curve ·adj A line described according to some low, and having no finite portion of it a straight line.
V. Curve ·adj To Bend; to Crook; as, to curve a line; to curve a pipe; to cause to swerve from a straight course; as, to curve a ball in pitching it.
curve         
I
n.
1) to describe, make a curve (the road makes a curve to the right)
2) to plot a curve ('to locate a curve by plotted points')
3) (teaching) to grade (AE), mark on a curve
4) a hairpin, horseshoe; sharp curve
II
v.
1) to curve sharply
2) (D; intr.) to curve to (to curve to the right)
curve         
I. n.
Bend. See curvature, 1.
II. v. a., v. n.
Bend, crook, inflect, turn, wind.

Βικιπαίδεια

Curve

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.

Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width."

This definition of a curve has been formalized in modern mathematics as: A curve is the image of an interval to a topological space by a continuous function. In some contexts, the function that defines the curve is called a parametrization, and the curve is a parametric curve. In this article, these curves are sometimes called topological curves to distinguish them from more constrained curves such as differentiable curves. This definition encompasses most curves that are studied in mathematics; notable exceptions are level curves (which are unions of curves and isolated points), and algebraic curves (see below). Level curves and algebraic curves are sometimes called implicit curves, since they are generally defined by implicit equations.

Nevertheless, the class of topological curves is very broad, and contains some curves that do not look as one may expect for a curve, or even cannot be drawn. This is the case of space-filling curves and fractal curves. For ensuring more regularity, the function that defines a curve is often supposed to be differentiable, and the curve is then said to be a differentiable curve.

A plane algebraic curve is the zero set of a polynomial in two indeterminates. More generally, an algebraic curve is the zero set of a finite set of polynomials, which satisfies the further condition of being an algebraic variety of dimension one. If the coefficients of the polynomials belong to a field k, the curve is said to be defined over k. In the common case of a real algebraic curve, where k is the field of real numbers, an algebraic curve is a finite union of topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is not a curve, but a surface, and is often called a Riemann surface. Although not being curves in the common sense, algebraic curves defined over other fields have been widely studied. In particular, algebraic curves over a finite field are widely used in modern cryptography.

Παραδείγματα από το σώμα κειμένου για Curve
1. The reversion to a more normally shaped yield curve continued, with the curve almost flat.
2. The Learning Curve Education, education, education.
3. Action at the short end of the US yield curve also sent three–year yields below two–year yields – the first sign of an inversion in the curve.
4. While the shape of the yield curve is very inverted, the absolute level of interest rates across the curve is not particularly high.
5. "It doesn‘t get me ahead of the curve, but helps make sure I‘m not run over by the curve," Klass said.