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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]
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. 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 .
Intersection of a sphere and cone emanating from its center. A spherical sector (blue) A spherical sector. In geometry, a spherical sector, [ 1] also known as a spherical cone, [ 2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and ...
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the cap is equal to the radius of the sphere, the spherical ...
Terminology for spherical segments. In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes . It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone .
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
A is the surface area of the spherical cap, , 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. By ...
Defined by Wadell in 1935, [ 1] the sphericity, , of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area: {\displaystyle \Psi = {\frac {\pi ^ {\frac {1} {3}} (6V_ {p})^ {\frac {2} {3}}} {A_ {p}}}} where is volume of the object and is the surface area. The sphericity of a sphere is unity by ...
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