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The pentagonal wegde is one of the seven topologically distinct convex hexahedra. Like the cube, it contains 8 vertices, 12 edges, and 6 faces, but its faces consist of 2 ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

A (symmetrical) boundary set of radius r and center x_0 is the set of all points x such that |x-x_0|=r. Let x_0 be the origin. In R^1, the boundary set is then the pair of ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...

Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

The Fourier transform of a Gaussian function f(x)=e^(-ax^2) is given by F_x[e^(-ax^2)](k) = int_(-infty)^inftye^(-ax^2)e^(-2piikx)dx (1) = ...

Kummer's first formula is (1) where _2F_1(a,b;c;z) is the hypergeometric function with m!=-1/2, -1, -3/2, ..., and Gamma(z) is the gamma function. The identity can be written ...

A tetradic (or four-way) number is a number that remains unchanged when flipped back to front, mirrored up-down, or flipped up-down. Since the only numbers that remain ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...