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A sphere (from Greek ... determined by the original two spheres. In this definition a sphere is allowed to be a plane (infinite radius, center at infinity) and if ...
It is called the 2-sphere, S 2, for reasons given below. The same idea applies for any dimension n; the equation x 2 0 + x 2 1 + ⋯ + x 2 n = 1 produces the n-sphere as a geometric object in (n + 1)-dimensional space. For example, the 1-sphere S 1 is a circle. [2] Disk with collapsed rim: written in topology as D 2 /S 1
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.
There are some variations of the definition of a Kleinian group: sometimes Kleinian groups are allowed to be subgroups of PSL(2, C).2 (that is, of PSL(2, C) extended by complex conjugations), in other words to have orientation reversing elements, and sometimes they are assumed to be finitely generated, and sometimes they are required to act properly discontinuously on a non-empty open subset ...
A Dyson sphere is a hypothetical megastructure that encompasses a star and captures a large percentage of its power output. [ 1 ] [ 2 ] [ 3 ] The concept is a thought experiment that attempts to imagine how a spacefaring civilization would meet its energy requirements once those requirements exceed what can be generated from the home planet's ...
Nine months after U2 wrapped its 40-date residency at Sphere, the veteran Irish rock band is back at the dome-shaped venue just off the Las Vegas Strip.. Well, sort of. “V-U2” is a new concert ...
If the sphere is isometrically embedded in Euclidean space, the sphere's intersection with a plane is a circle, which can be interpreted extrinsically to the sphere as a Euclidean circle: a locus of points in the plane at a constant Euclidean distance (the extrinsic radius) from a point in the plane (the extrinsic center). A great circle lies ...
President Vladimir Putin said on Thursday that the West would be directly fighting with Russia if it allowed Ukraine to strike Russian territory with Western-made long-range missiles, a move he ...