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The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

A projective module generalizes the concept of the free module. A module M over a nonzero unit ring R is projective iff it is a direct summand of a free module, i.e., of some ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

In combinatorial mathematics, the series-parallel networks problem asks for the number of networks that can be formed using a given number of edges. The edges can be ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

Riemann defined the function f(x) by f(x) = sum_(p^(nu)<=x; p prime)1/nu (1) = sum_(n=1)^(|_lgx_|)(pi(x^(1/n)))/n (2) = pi(x)+1/2pi(x^(1/2))+1/3pi(x^(1/3))+... (3) (Hardy ...