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In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [2] For a radius, , an open disk is usually denoted as and a closed disk is ¯.
is an example of a real analytic and bijective function from the open unit disk to the plane; its inverse function is also analytic. Considered as a real 2-dimensional analytic manifold, the open unit disk is therefore isomorphic to the whole plane. In particular, the open unit disk is homeomorphic to the whole plane.
In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine ...
Double density (DD) 3½-inch disks use an iron oxide coating, just as with 5¼-inch DD/QD disks. However, drives utilize stronger 670-oersted write heads and a narrower track width of 0.115 mm (0.0045 in) for a density of 135 tpi and 8,717 bpi. High density (HD) 3½-inch disks switch to a cobalt disk coating, just as with 5¼-inch HD disks ...
An example of this phenomenon is Dirichlet's theorem, to which it was originally applied by Heine, that a continuous function on a compact interval is uniformly continuous; here, continuity is a local property of the function, and uniform continuity the corresponding global property.
Hard disk drives store data in the magnetic polarization of small patches of the surface coating on a disk. The maximum areal density is defined by the size of the magnetic particles in the surface, as well as the size of the "head" used to read and write the data. In 1956 the first hard drive, the IBM 350, had an areal density of 2,000 bit/in 2.
In the case of a disk seen face-on, area density for a given area of the disk is defined as column density: that is, either as the mass of substance per unit area integrated along the vertical path that goes through the disk (line-of-sight), from the bottom to the top of the medium:
In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain line bundle , called the density bundle .