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The square-triangle theorem states that any nonnegative integer can be represented as the sum of a square, an even square, and a triangular number (Sun 2005), i.e., ...

A stochastic matrix, also called a probability matrix, probability transition matrix, transition matrix, substitution matrix, or Markov matrix, is matrix used to characterize ...

Multiple series generalizations of basic hypergeometric series over the unitary groups U(n+1). The fundamental theorem of U(n) series takes c_1, ..., c_n and x_1, ..., x_n as ...

Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation of degree n a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the roots are taken ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The augmented dodecahedron is Johnson solid J_(58), which is formed from augmentation of one of the faces of the regular dodecahedron by an equilateral pentagonal pyramid. It ...

A chamfered icosahedron, also called a tritruncated rhombic triacontahedron, is a polyhedron obtained by chamfering a regular icosahedron. The illustration above shows ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...