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3-sphere: In mathematics, a 3-sphere 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. Just as an ordinary 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.
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Printed dictionaries and other books with definitions for 3-sphere
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A Critique of Pure Physics (2009)
by Thomas Neil Neubert
Wikipedia explains as follows: A 3-sphere is a higher-dimensional analogue to a sphere . . . An ordinary sphere (or 2-sphere) is a two dimensional surface while a 3-sphere is an object with three dimensions.14 Likewise the macroscopic 3D ...
by Nikolai Saveliev
Conversely, a rational plumbed homology 3-sphere is a link of singularity if ...
by Timothy Gowers, June Barrow-Green, Imre Leader
Similarly, the 3-sphere is a 3-manifold. The formal definition of a manifold uses the ...
Disproof of Bell's Theorem (2014)
Illuminating the Illusion of Entanglement, Second Edition by Joy Christian
Proof: A 3-sphere is a set of points equidistant from a fixed point in IR4. Thus it is a boundary of a 4-ball in four dimensions. And as such, it is not the easiest space for us to visualize (although it is not impossible to do so ). Therefore, let us ...
Historical, Philosophical, and Scientific Foundations of Modern Cosmology by Norriss S. Hetherington
®3-sphere. ̄. Peterson suggests that the proportion between speed and size in the planetary and the angelic spheres constitutes a ...
by Peter Coles
respectively to the hyper- sphere (3-sphere), Euclidean three- dimensional space and a space of constant negative curvature (see curvature of spacetime). The geometrical properties of Euclidean space (k = 0) are well known.
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