Search Results for ""

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

Ramanujan's Dirichlet L-series is defined as f(s)=sum_(n=1)^infty(tau(n))/(n^s), (1) where tau(n) is the tau function. Note that the notation F(s) is sometimes used instead ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

An official chessboard is an 8×8 board containing squares alternating in color between olive green and buff (where "buff" is a color variously defined as a moderate orange ...

A game played with two dice. If the total is 7 or 11 (a "natural"), the thrower wins and retains the dice for another throw. If the total is 2, 3, or 12 ("craps"), the ...

The gnomon was an L-shaped movable sundial used for astronomical studies. It operated by resting on one leg so that the other pointed vertically upward. By measuring the ...

A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...

A labeled graph G=(V,E) is a finite series of graph vertices V with a set of graph edges E of 2-subsets of V. Given a graph vertex set V_n={1,2,...,n}, the number of ...