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It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

A set of m distinct positive integers S={a_1,...,a_m} satisfies the Diophantus property D(n) of order n (a positive integer) if, for all i,j=1, ..., m with i!=j, ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

Somos's quadratic recurrence constant is defined via the sequence g_n=ng_(n-1)^2 (1) with g_0=1. This has closed-form solution ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

The great icosahedron, not to be confused with the great icosidodecahedron orgreat icosicosidodecahedron, is the Kepler-Poinsot polyhedronhose dual is the great stellated ...

The great stellated dodecahedron is one of the Kepler-Poinsot polyhedra. It is also the uniform polyhedron with Maeder index 52 (Maeder 1997), Wenninger index 22 (Wenninger ...