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Squaring is the geometric construction, using only compass and straightedge, of a square which has the same area as a given geometric figure. Squaring is also called ...

Consider the Euler product zeta(s)=product_(k=1)^infty1/(1-1/(p_k^s)), (1) where zeta(s) is the Riemann zeta function and p_k is the kth prime. zeta(1)=infty, but taking the ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

The bivariate normal distribution is the statistical distribution with probability density function P(x_1,x_2)=1/(2pisigma_1sigma_2sqrt(1-rho^2))exp[-z/(2(1-rho^2))], (1) ...

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 ...