Search Results for ""

A number n is called equidigital if the number of digits in the prime factorization of n (including powers) uses the same number of digits as the number of digits in n. The ...

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 exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

The sum over all external (square) nodes of the lengths of the paths from the root of an extended binary tree to each node. For example, in the tree above, the external path ...

A Pascal's triangle written in a square grid and padded with zeros, as written by Jakob Bernoulli (Smith 1984). The figurate number triangle therefore has entries a_(ij)=(i; ...

A group is called a free group if no relation exists between its group generators other than the relationship between an element and its inverse required as one of the ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

A generalization of the equation whose solution is desired in Fermat's last theorem x^n+y^n=z^n to x^n+y^n=cz^n for x, y, z, and c positive constants, with trivial solutions ...