Search results
Results from the WOW.Com Content Network
a 0-sphere is a pair of points {, +} , and is the boundary of a line segment ( -ball). a 1-sphere is a circle of radius centered at , and is the boundary of a disk ( -ball).
The simplest axisymmetric shape is the sphere or spherical section. ... (324 °F) warmer than the normally sub-zero, ambient air); the metallurgical implications ...
In probability theory, a subgaussian distribution, the distribution of a subgaussian random variable, is a probability distribution with strong tail decay. More specifically, the tails of a subgaussian distribution are dominated by (i.e. decay at least as fast as) the tails of a Gaussian.
A sphere of radius r has area element = . This can be found from the volume element in spherical coordinates with r held constant. [9] A sphere of any radius centered at zero is an integral surface of the following differential form: + + =
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
Zero-dimensional Polish spaces are a particularly convenient setting for descriptive set theory. Examples of such spaces include the Cantor space and Baire space . Hausdorff zero-dimensional spaces are precisely the subspaces of topological powers 2 I {\displaystyle 2^{I}} where 2 = { 0 , 1 } {\displaystyle 2=\{0,1\}} is given the discrete ...
In dimensions 2 and 3 the Weyl tensor vanishes, but in 4 or more dimensions the Weyl tensor can be non-zero. For a manifold of constant curvature , the Weyl tensor is zero. Moreover, W = 0 {\displaystyle W=0} if and only if the metric is locally conformal to the Euclidean metric .