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Alternatively, the closely related mean diameter (), which is twice the mean radius, is also used. For a non-spherical object, the mean radius (denoted R {\displaystyle R} or r {\displaystyle r} ) is defined as the radius of the sphere that would enclose the same volume as the object. [ 1 ]
Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It is the three-dimensional equivalent of the circle packing in a circle problem in two dimensions.
For any natural number , an -sphere of radius is defined as the set of points in (+) -dimensional Euclidean space that are at distance from some fixed point , where may be any positive real number and where may be any point in (+) -dimensional space.
Mie Scattering from a sphere. x is the wave number times the sphere's radius and m is the refractive index of the sphere divided by the refractive index of the medium. In electromagnetism , the Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution , the Lorenz–Mie–Debye solution or Mie scattering ) describes the ...
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 ...
If a radius is extended through the center to the opposite side of the sphere, it creates a diameter. Like the radius, the length of a diameter is also called the diameter, and denoted d. Diameters are the longest line segments that can be drawn between two points on the sphere: their length is twice the radius, d = 2r. Two points on the sphere ...
The 3-sphere is homeomorphic to the one-point compactification of R 3. In general, any topological space that is homeomorphic to the 3-sphere is called a topological 3-sphere. The homology groups of the 3-sphere are as follows: H 0 (S 3, Z) and H 3 (S 3, Z) are both infinite cyclic, while H i (S 3, Z) = {} for all other indices i.
an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc) Thus, the angular diameter of Earth's orbit around the Sun as viewed from a distance of 1 pc is 2″, as 1 AU is the mean radius of Earth's orbit. The angular diameter of the Sun, from a distance of one light-year, is 0.03″, and that of Earth 0.0003″. The angular ...