Melk (older spelling: Mölk) is a city of Austria, in the federal state of Lower Austria, next to the Wachau valley along the Danube. Melk has a population of 5,257 (as of 2012). It is best known as the site of a massive baroque Benedictine monastery named Melk Abbey.
The town is first mentioned as Medilica in 831 in a donation of Louis the German; the name is from a Slavic word for 'border.' The area around Melk was given to Margrave Leopold I in the year 976 to serve as a buffer between the Magyars (called "Turks" in that time's sources) to east and Bavaria to the west. In 996 mention was first made of an area known as Ostarichi, which is the origin of the word Oesterreich (German for Austria). The bluff which holds the current monastery held a Babenberger castle until the site was given to Benedictine monks from nearby Lambach by Margrave Leopold II in 1089. Melk received market rights in 1227 and became a municipality in 1898. In a very small area, Melk presents a great deal of architectural variety from many centuries.
In mathematics, a curve (also called a curved line in older texts) 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 (plane curves) or three-dimensional (space curves) 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 (as in learning curve), or graph of a function (as in Phillips curve).