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The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

If one root of the equation f(x)=0, which is irreducible over a field K, is also a root of the equation F(x)=0 in K, then all the roots of the irreducible equation f(x)=0 are ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both ...

An equation for a lattice sum b_3(1) (Borwein and Bailey 2003, p. 26) b_3(1) = sum^'_(i,j,k=-infty)^infty((-1)^(i+j+k))/(sqrt(i^2+j^2+k^2)) (1) = ...

A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

A hypothetic building design problem in optimization with constraints proposed by Bhatti (2000, pp. 3-5). To save energy costs for heating and cooling, an architect wishes to ...