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Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation of degree n a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the roots are taken ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

A sequence {x_1,x_2,...} is equidistributed iff lim_(N->infty)1/Nsum_(n<N)e^(2piimx_n)=0 for each m=1, 2, .... A consequence of this result is that the sequence {frac(nx)} is ...

A run is a sequence of more than one consecutive identical outcomes, also known as a clump. Let R_p(r,n) be the probability that a run of r or more consecutive heads appears ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the ...

The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...