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In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in ...

A power series in a variable z is an infinite sum of the form sum_(i=0)^inftya_iz^i, where a_i are integers, real numbers, complex numbers, or any other quantities of a given ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the ...

The value for zeta(2)=sum_(k=1)^infty1/(k^2) (1) can be found using a number of different techniques (Apostol 1983, Choe 1987, Giesy 1972, Holme 1970, Kimble 1987, Knopp and ...