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The conical spiral with angular frequency a on a cone of height h and radius r is a space curve given by the parametric equations x = (h-z)/hrcos(az) (1) y = (h-z)/hrsin(az) ...

The contact angle between a sphere and a tangent plane is the angle alpha between the normal to the sphere at the point of tangency and the basal plane with respect to which ...

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

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

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.

Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is ...

A n-dipyramidal graph is the skeleton of an n-sided dipyramid. It is isomorphic to the (m,2)-cone graph C_m+K^__2, where C_m is a cycle graph, K^__2 is the empty graph on 2 ...