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In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 50-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

The 2-point Newton-Cotes formula int_(x_1)^(x_2)f(x)dx=1/2h(f_1+f_2)-1/(12)h^3f^('')(xi), where f_i=f(x_i), h is the separation between the points, and xi is a point ...

The triangle graph is the cycle graph C_3, which is isomorphic to the complete graph K_3 as well as to the complete tripartite graph K_(3×1)=K_(1,1,1) and the triangular ...

A truth table is a two-dimensional array with n+1 columns. The first n columns correspond to the possible values of n inputs, and the last column to the operation being ...

A unit matrix is an integer matrix consisting of all 1s. The m×n unit matrix is often denoted J_(mn), or J_n if m=n. Square unit matrices J_n have determinant 0 for n>=2. An ...

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...