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A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

There are several related series that are known as the binomial series. The most general is (x+a)^nu=sum_(k=0)^infty(nu; k)x^ka^(nu-k), (1) where (nu; k) is a binomial ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness under ...

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore ...

Long multiplication is the method of multiplication that is commonly taught to elementary school students throughout the world. It can be used on two numbers of arbitrarily ...

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

A binary operation f(x,y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1. f is ...