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A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a ...
Volumes of balls in dimensions 0 through 25; unit ball in red. In geometry, a ball is a region in a space comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An n-ball is a ball in an n-dimensional Euclidean space.
The volume of the unit ball in Euclidean -space, and the surface area of the unit sphere, appear in many important formulas of analysis. The volume of the unit n {\displaystyle n} -ball, which we denote V n , {\displaystyle V_{n},} can be expressed by making use of the gamma function .
For the small outer irregular moons of Uranus, such as Sycorax, which were not discovered by the Voyager 2 flyby, even different NASA web pages, such as the National Space Science Data Center [6] and JPL Solar System Dynamics, [5] give somewhat contradictory size and albedo estimates depending on which research paper is being cited.
The covering number quantifies the size of a set and can be applied to general metric spaces. Two related concepts are the packing number , the number of disjoint balls that fit in a space, and the metric entropy , the number of points that fit in a space when constrained to lie at some fixed minimum distance apart.
The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non ...
Typical size of a fog, mist, or cloud water droplet 10 μm Width of transistors in the Intel 4004, the world's first commercial microprocessor: 12 μm Width of acrylic fiber: 17–181 μm Width range of human hair [25] 10 −4: 100 μm: 340 μm Size of a pixel on a 17-inch monitor with a resolution of 1024×768 560 μm
In three dimensions, the kissing number is 12, but the correct value was much more difficult to establish than in dimensions one and two. It is easy to arrange 12 spheres so that each touches a central sphere, with a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere.