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An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...

The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The perimeter of a circle is called the ...

The nth Beraha constant (or number) is given by B(n)=2+2cos((2pi)/n). B(5) is phi+1, where phi is the golden ratio, B(7) is the silver constant, and B(10)=phi+2. The ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

The rational distance problem asks to find a geometric configuration satisfying given properties such that all distances along specific edges are rational numbers. (This is ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...