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The Weierstrass constant is defined as the value sigma(1|1,i)/2, where sigma(z|omega_1,omega_2) is the Weierstrass sigma function with half-periods omega_1 and omega_2. ...

Consider a symmetric triangle wave T(x) of period 2L. Since the function is odd, a_0 = 0 (1) a_n = 0, (2) and b_n = (3) = (32)/(pi^2n^2)cos(1/4npi)sin^3(1/4npi) (4) = ...

Let K be a field, and A a K-algebra. Elements y_1, ..., y_n are algebraically independent over K if the natural surjection K[Y_1,...,Y_n]->K[y_1,...,y_n] is an isomorphism. ...

An Archimedean circle is a circle defined in the arbelos in a natural way and congruent to Archimedes' circles, i.e., having radius rho=1/2r(1-r) for an arbelos with outer ...

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

Let g be a finite-dimensional Lie algebra over some field k. A subalgebra h of g is called a Cartan subalgebra if it is nilpotent and equal to its normalizer, which is the ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

For any sequence of integers 0<n_1<...<n_k, there is a flag manifold of type (n_1, ..., n_k) which is the collection of ordered sets of vector subspaces of R^(n_k) (V_1, ..., ...

The fourth group isomorphism theorem, also called the lattice group isomorphism theorem, lets G be a group and let N⊴G, where N⊴G indicates that N is a normal subgroup of G. ...

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...