Search results
Results From The WOW.Com Content Network
In mathematics, an n-sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer . The circle is considered 1-dimensional, and the sphere 2-dimensional, because the surfaces themselves are 1- and 2-dimensional respectively, not because they ...
The volume of the n-ball () can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial coordinate r and angular coordinates φ 1 , …, φ n − 1 , where the domain of each φ except φ n − 1 is [0, π ) , and the domain of φ n − 1 is [0, 2 π ) .
In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space , it is the set of points equidistant from a fixed central point.
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 ...
The 5-sphere, or hypersphere in six dimensions, is the five-dimensional surface equidistant from a point. It has symbol S 5, and the equation for the 5-sphere, radius r, centre the origin is = {: ‖ ‖ =}. The volume of six-dimensional space bounded by this 5-sphere is
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
hypersphere volume and surface area graphs: Image title: Graphs of volumes and surface areas of n-spheres of radius 1 by CMG Lee. The apparent intersection is an artifact of the differing scales. In the SVG file, hover over a point to see its decimal value. Width: 100%: Height: 100%
Very little is known about irregular hypersphere packings; it is possible that in some dimensions the densest packing may be irregular. Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing. [12]