linguistic:paraphrasing, information:filtering
Sphere

The sphere is an example of a surface. The unit sphere of implicit equation

may be covered by an atlas of six charts: the plane z = 0 divides the sphere into two half spheres (z > 0 and z < 0), which may both be mapped on the disc x + y < 1 by the projection on the xy plane of coordinates. This provides two charts; the four other charts are provided by a similar construction with the two other coordinate planes.

As with the circle, one may define one chart that covers the whole sphere excluding one point. Thus two charts are sufficient, but the sphere cannot be covered by a single chart.

This example is historically significant, as it has motivated the terminology; it became apparent that the whole surface of the Earth cannot have a plane representation consisting of a single map (also called "chart", see nautical chart), and therefore one needs atlases for covering the whole Earth surface.