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A number of attractive polyhedron compounds consisting of three octahedra. The first (left figues) is the polyhedron dual of the cube 3-compound. These compounds will be ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

One of the symbols ( or ) used to denote grouping. Parentheses have a great many specialized meanings in mathematics. A few of these are described below. 1. Parentheses are ...

An impossible figure in which a stairway in the shape of a square appears to circulate indefinitely while still possessing normal steps (Penrose and Penrose 1958). The Dutch ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

A quotient-difference table is a triangular array of numbers constructed by drawing a sequence of n numbers in a horizontal row and placing a 1 above each. An additional "1" ...

The rectangle function Pi(x) is a function that is 0 outside the interval [-1/2,1/2] and unity inside it. It is also called the gate function, pulse function, or window ...