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. A parabola [抛物线] is one of the simplest curves, after (straight lines.

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. 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.

While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines in two-dimensional space), there are obvious examples such as the helix which exist naturally in three dimensions. The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions.

In general relativity, a world line is a curve in spacetime.

In image editing, a curve is a remapping of image tonality, specified as a function from input level to output level, used as a way to emphasize colours or other elements in a picture. Curves can usually be applied to all channels together in an image, or to each channel individually. Applying a curve to all channels typically changes the brightness in part of the spectrum. Light parts of a picture can be easily made lighter and dark parts darker to increase contrast. Applying a curve to individual channels can be used to stress a colour. This is particularly efficient in the Lab colour space due to the separation of luminance and chromaticity, but it can also be used in RGB, CMYK or whatever other colour models the software supports.

In finance, the yield curve is a curve showing several yields to maturity or interest rates [利率] across different contract lengths (2 month, 2 year, 20 year, etc. ...) for a similar debt contract. The curve shows the relation between the (level of the) interest rate (or cost of borrowing) and the time to maturity, known as the "term", of the debt for a given borrower in a given currency.

六级/考研单词: mathematics, curve, trace, interval, perpetual, spiral, dimension, geometry, classic, mechanic, edit, spectrum, hardware, yield, mature