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The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. The spheres can be used to show that the ...
Any four mutually tangent spheres determine six points of tangency. A pair of tangencies (t_i,t_j) is said to be opposite if the two spheres determining t_i are distinct from ...
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 ...
The number of regions into which space can be divided by n mutually intersecting spheres is N=1/3n(n^2-3n+8), giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ...
Let a cone of opening parameter c and vertex at (0,0,0) intersect a sphere of radius r centered at (x_0,y_0,z_0), with the cone oriented such that its axis does not pass ...
A circular cone the centers of whose sections form a line perpendicular to the bases. When used without qualification, the term "cone" often refers to a right circular cone.
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; ...
One of the two pieces of a double cone (i.e., two cones placed apex to apex).
A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...
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 ...
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