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The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

Draw three circles in the plane, none of which lies completely inside another, and the common external tangent lines for each pair. Then points of intersection of the three ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

A sliver of the surface of a sphere of radius r cut out by two planes through the azimuthal axis with dihedral angle theta. The surface area of the lune is S=2r^2theta, which ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

A spherical polyhedron is set of arcs on the surface of a sphere corresponding to the projections of the edges of a polyhedron. The images above illustrate the spherical ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...