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There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

The Markov numbers m are the union of the solutions (x,y,z) to the Markov equation x^2+y^2+z^2=3xyz, (1) and are related to Lagrange numbers L_n by L_n=sqrt(9-4/(m^2)). (2) ...

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

A sequence of positive integers 1<=a_1<a_2<a_3<... (1) is a nonaveraging sequence if it contains no three terms which are in an arithmetic progression, i.e., terms such that ...

Let G be a simple graph with nonsingular (0,1) adjacency matrix A. If all the diagonal entries of the matrix inverse A^(-1) are zero and all the off-diagonal entries of ...

A "squashed" spheroid for which the equatorial radius a is greater than the polar radius c, so a>c (called an oblate ellipsoid by Tietze 1965, p. 27). An oblate spheroid is a ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...