2-sphere wireframe as an orthogonal projection Just as a stereographic projection can project a sphere's surface to a plane, it can also project the surface of a 3-sphere into 3-space. Source: Internet
As a 3-sphere moves through a given three-dimensional hyperplane, the intersection starts out as a point, then becomes a growing 2-sphere that reaches its maximal size when the hyperplane cuts right through the "equator" of the 3-sphere. Source: Internet
As with all spheres, the 3-sphere has constant positive sectional curvature equal to where is the radius. Source: Internet
An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence : if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it. Source: Internet
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. Source: Internet
For example, a Dehn filling with slope on any knot in the 3-sphere gives a homology sphere; typically these are not homeomorphic to the 3-sphere. Source: Internet