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The Stammler hyperbola of a triangle is the Feuerbach hyperbola of its tangential triangle, and its center is the focus of the Kiepert parabola, which is Kimberling center ...

A cubic map is three-colorable iff each interior region is bounded by an even number of regions. A non-cubic map bounded by an even number of regions is not necessarily ...

Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...

A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector v^^ having the same direction as a given ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...

A semiprime, also called a 2-almost prime, biprime (Conway et al. 2008), or pq-number, is a composite number that is the product of two (possibly equal) primes. The first few ...