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Handles and cross-handles are equivalent in the presence of a cross-cap.

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their automorphism groups.

"Exactly one" means "one and only one," sometimes also referred to as "just one" or "one and only one." J. H. Conway has also humorously suggested "onee" (one and only one) ...

In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the power sum of the first n positive integers, sum_(k=1)^(n)k^p = H_(n,-p) (1) = ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...

Let t be an infinite word over a finite alphabet Sigma. Then there exists a uniformly recurrent infinite word r such that Sub(r) subset= Sub(t), where Sub(w) is the set of ...

The Gallatly circle is the circle with center at the Brocard midpoint X_(39) and radius R_G = Rsinomega (1) = (abc)/(2sqrt(a^2b^2+a^2c^2+b^2c^2)), (2) where R is the ...

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

The general unitary group GU_n(q) is the subgroup of all elements of the general linear group GL(q^2) that fix a given nonsingular Hermitian form. This is equivalent, in the ...