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A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...

A centered polygonal number consisting of a central dot with four dots around it, and then additional dots in the gaps between adjacent dots. The general term is n^2+(n+1)^2, ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

A golden rhombohedron is a rhombohedron whose faces consist of congruent golden rhombi. Golden rhombohedra are therefore special cases of a trigonal trapezohedron as well as ...

Let A_(k,i)(n) denote the number of partitions into n parts not congruent to 0, i, or -i (mod 2k+1). Let B_(k,i)(n) denote the number of partitions of n wherein 1. 1 appears ...

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

A dissection of a rectangle into smaller rectangles such that the original rectangle is not divided into two subrectangles. Rectangle dissections into 3, 4, or 6 pieces ...