Search Results for ""

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

The necker cube is an illusion in which a two-dimensional drawing of an array of cubes appears to simultaneously protrude from and intrude into the page. A Necker cube ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

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

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

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 ...

"The" square graphs is the cycle graph C_4. It is isomorphic to the complete bipartite graph K_(2,2). Like all cycle graphs, the line graph of C_4 is isomorphic to itself. A ...

The tangential triangle is the triangle DeltaT_AT_BT_C formed by the lines tangent to the circumcircle of a given triangle DeltaABC at its vertices. It is therefore antipedal ...

A number of attractive tetrahedron 5-compounds can be constructed. The first (left figures) is one of the icosahedron stellations in which the 5×4 vertices of the tetrahedra ...

Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...