Concept
Ball (mathematics)
Related concepts (28)
Hamming distance
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or the minimum number of errors that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences.
Spherical cap
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. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere.
Volume of an n-ball
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 a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n-ball of radius R is where is the volume of the unit n-ball, the n-ball of radius 1.
Spherical segment
In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone. If the radius of the sphere is called R, the radii of the spherical segment bases are r_1 and r_2, and the height of the segment (the distance from one parallel plane to the other) called h, then the
Spherical wedge
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base). The angle between the radii lying within the bounding semidisks is the dihedral α. If AB is a semidisk that forms a ball when completely revolved about the z-axis, revolving AB only through a given α produces a spherical wedge of the same angle α. Beman (2008) remarks that "a spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon.
Euclidean topology
In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on -dimensional Euclidean space by the Euclidean metric. The Euclidean norm on is the non-negative function defined by Like all norms, it induces a canonical metric defined by The metric induced by the Euclidean norm is called the Euclidean metric or the Euclidean distance and the distance between points and is In any metric space, the open balls form a base for a topology on that space.
Chebyshev distance
In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board.
Spherical sector
In geometry, a spherical sector, also known as a spherical cone, is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of the sector of a circle. If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is This may also be written as where φ is half the cone angle, i.