Editing 3-sphere (section)

{{Short description|Mathematical object}}
{{more footnotes|date=June 2016}}
[[Image:Hypersphere coord.PNG|thumb|[[Stereographic projection]] of the hypersphere's parallels (red), meridians 
(blue) and hypermeridians (green).  Because this projection is [[conformal map|conformal]], the curves intersect each other orthogonally (in the yellow points) as in 4D.  All curves are circles: the curves that intersect {{angbr|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.]]
[[Image:Hypersphere.png|thumb|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|''n''-sphere]]. In 4-dimensional [[Euclidean space]], it is the set of points equidistant from a fixed central point. The interior of a 3-sphere is a '''4-ball'''.

It is called a 3-sphere because topologically, the surface itself is 3-dimensional, even though it is curved into the 4th dimension. For example, when traveling on a 3-sphere, you can go north and south, east and west, or along a 3rd set of cardinal directions. This means that a 3-sphere is an example of a [[3-manifold]].