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Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, Rn), axes (lines through the origin in Rn) or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds including the ...
The intersection of a sphere with an elliptic or hyperbolic cylinder whose axis passes through the sphere center. The locus of points whose sum or difference of great-circle distances from a pair of foci is a constant. Many theorems relating to planar conic sections also extend to spherical conics.
Ball (mathematics) In Euclidean space, a ball is the volume bounded by a sphere. In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. [1] It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three ...
Spherical mean. The spherical mean of a function (shown in red) is the average of the values (top, in blue) with on a "sphere" of given radius around a given point (bottom, in blue). In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that point.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distance r along the radial line connecting the point to the fixed point of origin; the polar angle θ between the radial line and a polar axis; and the ...
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. More generally, the unit -sphere is an -sphere of unit radius in - dimensional Euclidean space; the unit circle is a special case, the unit -sphere in the plane.
Spherical trigonometry. The octant of a sphere is a spherical triangle with three right angles. Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles.