This crossword clue is for the definition: Sphere.
it’s A 6 letters crossword puzzle definition.
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Possible Answers: ORB.
Last seen on: LA Times Crossword 13 Apr 2018, Friday
Random information on the term “Sphere”:
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in 4-dimensional Euclidean space. Analogous to how an ordinary sphere (or 2-sphere) is a two-dimensional surface that forms the boundary of a ball in three dimensions, a 3-sphere is an object with three dimensions that forms the boundary of a ball in four dimensions. A 3-sphere is an example of a 3-manifold.
In coordinates, a 3-sphere with center (C0, C1, C2, C3) and radius r is the set of all points (x0, x1, x2, x3) in real, 4-dimensional space (R4) such that
The 3-sphere centered at the origin with radius 1 is called the unit 3-sphere and is usually denoted S3:
It is often convenient to regard R4 as the space with 2 complex dimensions (C2) or the quaternions (H). The unit 3-sphere is then given by
This description as the quaternions of norm one, identifies the 3-sphere with the versors in the quaternion division ring. Just as the unit circle is important for planar polar coordinates, so the 3-sphere is important in the polar view of 4-space involved in quaternion multiplication. See polar decomposition of a quaternion for details of this development of the three-sphere. This view of the 3-sphere is the basis for the study of elliptic space as developed by Georges Lemaître.
Random information on the term “ORB”:
A sphere (from Greek σφαῖρα — sphaira, “globe, ball”) is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to a circular object in two dimensions).
Like a circle, which geometrically is an object in two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of the (sphere) ball.
While outside mathematics the terms “sphere” and “ball” are sometimes used interchangeably, in mathematics a distinction is made between the sphere (a two-dimensional closed surface embedded in three-dimensional Euclidean space) and the ball (a three-dimensional shape that includes the sphere as well as everything inside the sphere). This distinction has not always been maintained and there are mathematical references, especially older ones, that talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms “circle” and “disk” are confounded.