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A surface with boundary is a topological space obtained by identifying edges and vertices of a set of triangles according to all the requirements of a surface except that ...

The tangram is a combination of plane polygonal pieces such that the edges of the polygons are coincident. There are 13 convex tangrams (where a "convex tangram" is a set of ...

A topological space M satisfying some separability (i.e., it is a T2-space) and countability (i.e., it is a paracompact space) conditions such that every point p in M has a ...

Let m_1, m_2, ..., m_n be distinct primitive elements of a two-dimensional lattice M such that det(m_i,m_(i+1))>0 for i=1, ..., n-1. Each collection Gamma={m_1,m_2,...,m_n} ...

A brute-force method of finding a divisor of an integer n by simply plugging in one or a set of integers and seeing if they divide n. Repeated application of trial division ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that there is only one object fulfilling given properties, or ...

A unit ring is a ring with a multiplicative identity. It is therefore sometimes also known as a "ring with identity." It is given by a set together with two binary operators ...