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A magic hexagon of order n is an arrangement of close-packed hexagons containing the numbers 1, 2, ..., H_(n-1), where H_n is the nth hex number such that the numbers along ...

The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown ...

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also. This axiom is equivalent to the ...

Two or more lines or line segments which are perpendicular are said to be orthogonal.

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 ...

Consider the length of the diagonal of a unit square as approximated by piecewise linear steps that may only be taken in the right and up directions. Obviously, the length so ...

A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...