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Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The Feigenbaum constant delta is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

A graph G is hypohamiltonian if G is nonhamiltonian, but G-v is Hamiltonian for every v in V (Bondy and Murty 1976, p. 61). The Petersen graph, which has ten nodes, is the ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

The partial differential equation u_t+u_(xxx)-6uu_x=0 (1) (Lamb 1980; Zwillinger 1997, p. 175), often abbreviated "KdV." This is a nondimensionalized version of the equation ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...