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The bound for the number of colors which are sufficient for map coloring on a surface of genus g, gamma(g)=|_1/2(7+sqrt(48g+1))_| is the best possible, where |_x_| is the ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

A type of integral containing gamma functions in its integrand. A typical such integral is given by ...

The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties. Pathological problems ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

The rectangle function Pi(x) is a function that is 0 outside the interval [-1/2,1/2] and unity inside it. It is also called the gate function, pulse function, or window ...