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Sphere. A sphere (from Greek σφαῖρα, sphaîra) [1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [2]
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two- dimensional surface of a sphere [a] or the n -dimensional surface of higher dimensional spheres . Long studied for its practical applications to astronomy, navigation, and geodesy, spherical geometry and the metrical tools of spherical trigonometry ...
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 numbers, ( r, θ, φ ): the radial distance of the radial line r connecting the point to the fixed point of origin (which is located on a fixed polar axis, or zenith direction axis ...
r is the radius of the sphere, h is the height of the cap, and; sr is the unit, steradian. Because the surface area A of a sphere is 4πr 2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its centre, or that a steradian subtends 1/4π ≈ 0.07958 of a sphere.
The biosphere (from Greek βίος bíos "life" and σφαῖρα sphaira "sphere"), also known as the ecosphere (from Greek οἶκος oîkos "environment" and σφαῖρα), is the worldwide sum of all ecosystems. It can also be termed the zone of life on Earth. The biosphere (which is technically a spherical shell) is virtually a closed ...
Atmosphere. An atmosphere (from Ancient Greek ἀτμός (atmós) 'vapour, steam', and σφαῖρα (sphaîra) 'sphere') [1] is a layer of gasses that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low.
Sphericity is a measure of how closely the shape of an object resembles that of a perfect sphere. For example, the sphericity of the balls inside a ball bearing determines the quality of the bearing, such as the load it can bear or the speed at which it can turn without failing. Sphericity is a specific example of a compactness measure of a shape.
The n -sphere is the setting for n -dimensional spherical geometry . Considered extrinsically, as a hypersurface embedded in (n + 1) -dimensional Euclidean space, an n -sphere is the locus of points at equal distance (the radius) from a given center point. Its interior, consisting of all points closer to the center than the radius, is an (n + 1 ...