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Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

The real projective plane is the closed topological manifold, denoted RP^2, that is obtained by projecting the points of a plane E from a fixed point P (not on the plane), ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

Let DeltaABC be a triangle and D a point on the side BC. Let I be the incenter, P the center of the circle tangent to the circumcircle and segments AD and BD, Q the center of ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A graph G on more than two vertices is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a vertex cut of size k-1 whose removal ...

Scan the decimal expansion of a constant (including any digits to the left of the decimal point) until all n-digit strings have been seen (including 0-padded strings). The ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...