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Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point.
The idea of the great chain, as well as the derived "missing link", was abandoned in early 20th-century science, [23] as the notion of modern animals representing ancestors of other modern animals was abandoned in biology, to be replaced by an evolutionary tree supplemented by horizontal gene transfer, as well as more complex web structures. [24]
If p, q, and r are pairwise relatively prime positive integers then the link of the singularity x p + y q + z r = 0 (in other words, the intersection of a small 3-sphere around 0 with this complex surface) is a Brieskorn manifold that is a homology 3-sphere, called a Brieskorn 3-sphere Σ(p, q, r).
There are two possibilities: if =, the spheres coincide, and the intersection is the entire sphere; if , the spheres are disjoint and the intersection is empty. When a is nonzero, the intersection lies in a vertical plane with this x-coordinate, which may intersect both of the spheres, be tangent to both spheres, or external to both spheres.
In neo-Calvinism, sphere sovereignty (Dutch: soevereiniteit in eigen kring), also known as differentiated responsibility, is the concept that each sphere (or sector) of life has its own distinct responsibilities and authority or competence, and stands equal to other spheres of life. Sphere sovereignty involves the idea of an all-encompassing ...
Embedded contact homology, due to Michael Hutchings, is an invariant of 3-manifolds (with a distinguished second homology class, corresponding to the choice of a spin c structure in Seiberg–Witten Floer homology) isomorphic (by work of Clifford Taubes) to Seiberg–Witten Floer cohomology and consequently (by work announced by Kutluhan, Lee ...
Three spheres, triple spheres, and related terms may refer to: Architecture ... Science. Triple star system, a star system comprised of three stars; Symbols
In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through the center. In the intrinsic approach, a great circle is a geodesic; a shortest path between any two of its points provided they are close enough. Or, in the (also intrinsic) axiomatic approach analogous to Euclid's axioms of plane ...