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Let A_(k,i)(n) denote the number of partitions into n parts not congruent to 0, i, or -i (mod 2k+1). Let B_(k,i)(n) denote the number of partitions of n wherein 1. 1 appears ...

Various handshaking problems are in circulation, the most common one being the following. In a room of n people, how many different handshakes are possible? The answer is (n; ...

Minesweeper is single-player logic-based computer game played on rectangular board whose object is to locate a predetermined number of randomly-placed "mines" in the shortest ...

Let p={a_1,a_2,...,a_n} be a permutation. Then i is a permutation ascent if a_i<a_(i+1). For example, the permutation {1,2,3,4} is composed of three ascents, namely {1,2}, ...

Let f(x) be integrable in [-1,1], let (1-x^2)f(x) be of bounded variation in [-1,1], let M^' denote the least upper bound of |f(x)(1-x^2)| in [-1,1], and let V^' denote the ...

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...

The William Lowell Putnam Mathematics Competition is an annual mathematics contest open to North American college students administered by the Mathematical Association of ...

The quaternion group is one of the two non-Abelian groups of the five total finite groups of order 8. It is formed by the quaternions +/-1, +/-i, +/-j, and +/-k , denoted Q_8 ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m+1 points and fits all polynomials to degree 2m, so it effectively fits exactly all ...

A right angle is an angle equal to half the angle from one end of a line segment to the other. A right angle is pi/2 radians or 90 degrees. A triangle containing a right ...