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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 ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a ...

A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The spherical sector may either be "open" and have a conical hole (left figure; ...

Cohomotopy groups are similar to homotopy groups. A cohomotopy group is a group related to the homotopy classes of maps from a space X into a sphere S^n.

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.

In space, the only conformal mappings are inversions, similarity transformations, and congruence transformations. Or, restated, every angle-preserving transformation is a ...

A line of constant longitude on a spheroid (or sphere). More generally, a meridian of a surface of revolution is the intersection of the surface with a plane containing the ...