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If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i.e., (b-c)/m is an integer), then b and c are said to be "congruent ...

The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...

Let rho be a reciprocal difference. Then Thiele's interpolation formula is the continued fraction f(x)=f(x_1)+(x-x_1)/(rho(x_1,x_2)+)(x-x_2)/(rho_2(x_1,x_2,x_3)-f(x_1)+) ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal ...

Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...