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The reciprocal of the arithmetic-geometric mean of 1 and sqrt(2), G = 2/piint_0^11/(sqrt(1-x^4))dx (1) = 2/piint_0^(pi/2)(dtheta)/(sqrt(1+sin^2theta)) (2) = L/pi (3) = ...

Brocard's problem asks to find the values of n for which n!+1 is a square number m^2, where n! is the factorial (Brocard 1876, 1885). The only known solutions are n=4, 5, and ...

What is the maximum number of queens that can be placed on an n×n chessboard such that no two attack one another? The answer is n-1 queens for n=2 or n=3 and n queens ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...

A perfect graph is a graph G such that for every induced subgraph of G, the clique number equals the chromatic number, i.e., omega(G)=chi(G). A graph that is not a perfect ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

A repunit is a number consisting of copies of the single digit 1. The term "repunit" was coined by Beiler (1966), who also gave the first tabulation of known factors. In ...

cos(pi/(10)) = 1/4sqrt(10+2sqrt(5)) (1) cos((3pi)/(10)) = 1/4sqrt(10-2sqrt(5)) (2) cot(pi/(10)) = sqrt(5+2sqrt(5)) (3) cot((3pi)/(10)) = sqrt(5-2sqrt(5)) (4) csc(pi/(10)) = ...

cos(pi/(15)) = 1/8(sqrt(30+6sqrt(5))+sqrt(5)-1) (1) cos((2pi)/(15)) = 1/8(sqrt(30-6sqrt(5))+sqrt(5)+1) (2) cos((4pi)/(15)) = 1/8(sqrt(30+6sqrt(5))-sqrt(5)+1) (3) ...

cos(pi/(16)) = 1/2sqrt(2+sqrt(2+sqrt(2))) (1) cos((3pi)/(16)) = 1/2sqrt(2+sqrt(2-sqrt(2))) (2) cos((5pi)/(16)) = 1/2sqrt(2-sqrt(2-sqrt(2))) (3) cos((7pi)/(16)) = ...