curvekɜrv
curve (v)
- present
- curves
- past
- curved
- past participle
- curved
- present participle
- curving
curve
curve
English Definitions:
curve, curved shape (noun)
the trace of a point whose direction of motion changes
curve (noun)
a line on a graph representing data
curve, curve ball, breaking ball, bender (noun)
a pitch of a baseball that is thrown with spin so that its path curves as it approaches the batter
curvature, curve (noun)
the property possessed by the curving of a line or surface
bend, curve (verb)
curved segment (of a road or river or railroad track etc.)
swerve, sheer, curve, trend, veer, slue, slew, cut (verb)
turn sharply; change direction abruptly
"The car cut to the left at the intersection"; "The motorbike veered to the right"
wind, twist, curve (verb)
extend in curves and turns
"The road winds around the lake"; "the path twisted through the forest"
arch, curve, arc (verb)
form an arch or curve
"her back arches"; "her hips curve nicely"
crook, curve (verb)
bend or cause to bend
"He crooked his index finger"; "the road curved sharply"
curl, curve, kink (verb)
form a curl, curve, or kink
"the cigar smoke curled up at the ceiling"
curve (Noun)
A gentle bend, such as in a road.
curve (Noun)
A simple figure containing no straight portions and no angles; a curved line.
curve (Noun)
A grading system based on the scale of performance of a group used to normalize a right-skewed grade distribution (with more lower scores) into a bell curve, so that more can receive higher grades, regardless of their actual knowledge of the subject.
curve (Noun)
A continuous map from a one-dimensional space to a multidimensional space.
curve (Noun)
A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.
curve (Noun)
An algebraic curve; a polynomial relation of the planar coordinates.
curve (Noun)
A one-dimensional continuum.
curve (Noun)
(informal, usually in plural curves) The attractive shape of a woman's body.
curve (Verb)
To bend; to crook.
curve (Verb)
To cause to swerve from a straight course.
curve (Verb)
To bend or turn gradually from a given direction.
curve (Verb)
To grade on a curve (bell curve of a normal distribution).
curve (Adjective)
Bent without angles; crooked; curved.
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional or three-dimensional Euclidean space are of interest. Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields. The term curve has several meanings in non-mathematical language as well. For example, it can be almost synonymous with mathematical function, or graph of a function. An arc or segment of a curve is a part of a curve that is bounded by two distinct end points and contains every point on the curve between its end points. Depending on how the arc is defined, either of the two end points may or may not be part of it. When the arc is straight, it is typically called a line segment.
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.
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"curve." Kamus.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.kamus.net/english/curve>.
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