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The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common ...

The cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1,...,x_n} are the terms f_1 <= x_1<=g_1 (1) f_2(x_1) <= x_2<=g_2(x_1) (2) | ...

The dilogarithm Li_2(z) is a special case of the polylogarithm Li_n(z) for n=2. Note that the notation Li_2(x) is unfortunately similar to that for the logarithmic integral ...

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...

A domatic partition is a partition of the vertices of a graph into disjoint dominating sets. The maximum number of disjoint dominating sets in a domatic partition of a graph ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...