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A sphere with three handles (and three holes), i.e., a genus-3 torus.

The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

Find the surface enclosing the maximum volume per unit surface area, I=V/S. The solution is a sphere, which has I_(sphere)=(4/3pir^3)/(4pir^2)=1/3r. The fact that a sphere ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

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

A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.

A parabolic cyclide formed by inversion of a horn torus when the inversion sphere is tangent to the torus.

A parabolic cyclide formed by inversion of a ring torus when the inversion sphere is tangent to the torus.

A parabolic cyclide formed by inversion of a spindle torus when the inversion sphere is tangent to the torus.