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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 ...

An orthogonal projection of a cross onto a three-dimensional subspace. It is said to be normalized if the cross vectors are all of unit length.

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it ...

Two vectors u and v are parallel if their cross product is zero, i.e., uxv=0.

Any two ranges {ABC...} and {A^'B^'C^'...} which are situated on the same or different lines are said to be homographic when the cross ratio of any four points on one range ...

Line segment ranges and pencils which have equal cross ratios are said to be equicross.

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

A capsule is a term coined here for a stadium of revolution, i.e., a cylinder with two hemispherical caps on either end. The capsule is implemented in the Wolfram Language as ...

A bundle or fiber bundle is trivial if it is isomorphic to the cross product of the base space and a fiber.