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A topological two-sphere in three-space whose exterior is not simply connected. The outer complement of Antoine's horned sphere is not simply connected. Furthermore, the ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

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 ...

The map which takes points on the surface of a sphere S^2 to their antipodal points.

A cylindrical projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cylinder tangent to the sphere at ...

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

Spherical triangles into which a sphere is divided by the planes of symmetry of a uniform polyhedron.

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