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(geometry) The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more dimensions.

Stereographic projection of the hypersphere's parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles: the curves that intersect ⟨0,0,0,1⟩ have infinite radius (= straight line). In this picture, the whole 3D space maps the surface of the hypersphere, whereas in the next picture the 3D space contained the shadow of the bulk hypersphere.

(geometry) The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more dimensions.

Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres)

(geometry) The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more dimensions.

The Hopf fibration can be visualized using a stereographic projection of S3 to R3 and then compressing R3 to a ball. This image shows points on S2 and their corresponding fibers with the same color.