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A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is known as the ...

Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form M×V, where M is a four ...

A camel graph is a graph formed by all possible moves of a hypothetical chess piece called a "camel" which moves analogously to a knight except that it is restricted to moves ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping, every person ...

The ancient Greeks used the 24 letters of their alphabet plus three special signs called episemons--vau or digamma or stigma (6), koppa or qoppa (90), and san or sampi ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...