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Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving ...

A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

Let V be a real vector space (e.g., the real continuous functions C(I) on a closed interval I, two-dimensional Euclidean space R^2, the twice differentiable real functions ...

The complex lattice Lambda_6^omega corresponding to real lattice K_(12) having the densest hypersphere packing (kissing number) in twelve dimensions. The associated ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

For a nonzero real number r and a triangle DeltaABC, swing line segment BC about the vertex B towards vertex A through an angle rB. Call the line along the rotated segment L. ...