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As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

The Bernoulli distribution is a discrete distribution having two possible outcomes labelled by n=0 and n=1 in which n=1 ("success") occurs with probability p and n=0 ...

A reduction system is called confluent (or globally confluent) if, for all x, u, and w such that x->_*u and x->_*w, there exists a z such that u->_*z and w->_*z. A reduction ...

A number of attractive cube 6-compounds can be constructed. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining ...