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The statistical treatment of such data is in the realm of directional statistics. [ 1 ] The fact that 0 degrees and 360 degrees are identical angles , so that for example 180 degrees is not a sensible mean of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data ...
The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m -1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus.
The sphere has the smallest total mean curvature among all convex solids with a given surface area. The mean curvature is the average of the two principal curvatures, which is constant because the two principal curvatures are constant at all points of the sphere. The sphere has constant mean curvature.
Elliptical distribution. In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso ...
Concentration of measure. In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random variable that depends in a Lipschitz way on many independent variables (but ...
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 ...
Unlike a probability, a probability density function can take on values greater than one; for example, the continuous uniform distribution on the interval [0, 1/2] has probability density f(x) = 2 for 0 ≤ x ≤ 1/2 and f(x) = 0 elsewhere. The standard normal distribution has probability density. If a random variable X is given and its ...
The distance of the surface from the origin indicates the absolute value of in angular direction . In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields.