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Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

The Feller-Tornier constant is the density of integers that have an even number of prime factors p_i^(a_i) with a_1>1 in their prime factorization. It is given by ...

A problem listed in a fall issue of Gazeta Matematică in the mid-1970s posed the question if x_1>0 and x_(n+1)=(1+1/(x_n))^n (1) for n=1, 2, ..., then are there any values ...

Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b+1 (i.e., B[b] is a ...

Jenny's constant is the name given (Munroe 2012) to the positive real constant defined by J = (7^(e-1/e)-9)pi^2 (1) = 867.53090198... (2) (OEIS A182369), the first few digits ...

The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

A monotone triangle (also called a strict Gelfand pattern or a gog triangle) of order n is a number triangle with n numbers along each side and the base containing entries ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

A number of graphs are associated with P. J. Owens. The 76-node Owens graph (Owens 1980) provides the smallest known example of a polyhedral quintic nonhamiltonian graph. It ...

A power mean is a mean of the form M_p(a_1,a_2,...,a_n)=(1/nsum_(k=1)^na_k^p)^(1/p), (1) where the parameter p is an affinely extended real number and all a_k>=0. A power ...