Search Results for ""

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 ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...

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 formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

A generalization of the polyominoes using a collection of equal-sized equilateral triangles (instead of squares) arranged with coincident sides. Polyiamonds are sometimes ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

A polyomino tiling is a tiling of the plane by specified types of polyominoes. Tiling by polyominoes has been investigated since at least the late 1950s, particularly by S. ...

There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

A quadratic form Q(z) is said to be positive definite if Q(z)>0 for z!=0. A real quadratic form in n variables is positive definite iff its canonical form is ...