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Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

A Dedekind ring is a commutative ring in which the following hold. 1. It is a Noetherian ring and a integral domain. 2. It is the set of algebraic integers in its field of ...

An equation representing a locus L in the n-dimensional Euclidean space. It has the form L:f(x_1,...,x_n)=0, (1) where the left-hand side is some expression of the Cartesian ...

A standard basis, also called a natural basis, is a special orthonormal vector basis in which each basis vector has a single nonzero entry with value 1. In n-dimensional ...

If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...

Every convex body B in the Euclidean plane with area A can be inscribed in a triangle of area at most equal to 2A (Gross 1918, Eggleston 1957). The worst possible fit ...

A G-space provides local notions of harmonic, hyperharmonic, and superharmonic functions. When there exists a nonconstant superharmonic function greater than 0, it is a ...

Let f(z) be an analytic function in an angular domain W:|argz|<alphapi/2. Suppose there is a constant M such that for each epsilon>0, each finite boundary point has a ...

The set of prime numbers, sometimes denoted P (Derbyshire 2004, p. 163), and implemented in the Wolfram Language as Primes. In the Wolfram Language, a quantity can be tested ...