Search Results for ""

There are a number of attractive polyhedron compounds consisting of 25 octahedra. These compounds will be implemented in a future version of the Wolfram Language as ...

A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation x = (asin[(m+n)t])/(sin[(m-n)t]) (1) y = ...

The space of currents arising from rectifiable sets by integrating a differential form is called the space of two-dimensional rectifiable currents. For C a closed bounded ...

The inverse curve of a right strophoid with parametric equations x = (1-t^2)/(t^2+1) (1) y = (t(t^2-1))/(t^2+1) (2) for an inversion circle with radius 1 and center (1,0) is ...

Given a sequence of values {a_k}_(k=1)^n, the running maxima are the sequence of values {max(a_1,...,a_k)}_(k=1)^n. So, for example, given a sequence (3,5,7,8,8,5,7,9,2,5), ...

The sum of the absolute squares of the spherical harmonics Y_l^m(theta,phi) over all values of m is sum_(m=-l)^l|Y_l^m(theta,phi)|^2=(2l+1)/(4pi). (1) The double sum over m ...

A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that x = x(u,v) (1) y = y(u,v) (2) z = z(u,v). (3) If a surface is parameterized as ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

A transversal design TD_lambda(k,n) of order n, block size k, and index lambda is a triple (V, G, B) such that 1. V is a set of kn elements, 2. G is a partition of V into k ...