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Also called Chvátal's art gallery theorem. If the walls of an art gallery are made up of n straight line segments, then the entire gallery can always be supervised by |_n/3_| ...

Given a planar graph G, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent (Harary 1994), so that one may speak of ...

The Eisenstein integers, sometimes also called the Eisenstein-Jacobi integers (Finch 2003, p. 601), are numbers of the form a+bomega, where a and b are normal integers, ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

Euclid's second theorem states that the number of primes is infinite. The proof of this can be accomplished using the numbers E_n = 1+product_(i=1)^(n)p_i (1) = 1+p_n#, (2) ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...

The Hilbert curve is a Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling function which fills a square. Traversing the polyhedron vertices of an ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...