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Two cones placed base-to-base. The bicone with base radius r and half-height h has surface area and volume S = 2pirsqrt(r^2+h^2) (1) V = 2/3pir^2h. (2) The centroid is at the ...

The finite Fourier cosine transform of an apodization function, also known as an apparatus function. The instrument function I(k) corresponding to a given apodization ...

The pentagonal rotunda is a convex polyhedron consisting of half of an icosidodecahedron, with the base being filled in by a decagon. It has 10 triangular and five pentagonal ...

In the Wolfram Language, WignerD[{j, m ,n}, psi, theta, phi] gives the m×n matrix element of a (2j+1)-dimensional unitary representation of SU(2) parametrized by three Euler ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

Diophantus's riddle is a poem that encodes a mathematical problem. In verse, it read as follows: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone ...

A plane-filling arrangement of plane figures or its generalization to higher dimensions. Formally, a tiling is a collection of disjoint open sets, the closures of which cover ...

A surface that contains two families of rulings. The only three doubly ruled surfaces are the plane, hyperbolic paraboloid, and single-sheeted hyperboloid.

A symmetric design is a block design (v, k, lambda, r, b) with the same number of blocks as points, so b=v (or, equivalently, r=k). An example of a symmetric block design is ...

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, ...