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A quintic nonhamiltonian graph is a quintic graph that is nonhamiltonian. A number of such graphs are illustrated above. Owens (1980) showed that there exists a ...

Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

A random graph is a graph in which properties such as the number of graph vertices, graph edges, and connections between them are determined in some random way. The graphs ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

The Remez algorithm (Remez 1934), also called the Remez exchange algorithm, is an application of the Chebyshev alternation theorem that constructs the polynomial of best ...

Given the closed interval [0,x] with x>1, let one-dimensional "cars" of unit length be parked randomly on the interval. The mean number M(x) of cars which can fit (without ...

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

There are a number of equations known as the Riccati differential equation. The most common is z^2w^('')+[z^2-n(n+1)]w=0 (1) (Abramowitz and Stegun 1972, p. 445; Zwillinger ...