Search Results for ""

Consider the solid enclosed by the three hyperboloids specified by the inequalities x^2+y^2-z^2 <= 1 (1) y^2+z^2-x^2 <= 1 (2) z^2+x^2-y^2 <= 1. (3) This work dubs this solid ...

A twin prime cluster of order n is a collection of 2n consecutive prime numbers such that consecutive pairs form twin primes. Twin prime clusters were discussed by Mudge ...

The distribution for the sum X_1+X_2+...+X_n of n uniform variates on the interval [0,1] can be found directly as (1) where delta(x) is a delta function. A more elegant ...

The uniformity conjecture postulates a relationship between the syntactic length of expressions built up from the natural numbers using field operations, exponentials, and ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

The simple process of voting leads to surprisingly counterintuitive paradoxes. For example, if three people vote for three candidates, giving the rankings A, B, C; B, C, A; ...

An exponential sum of the form sum_(n=1)^Ne^(2piiP(n)), (1) where P(n) is a real polynomial (Weyl 1914, 1916; Montgomery 2001). Writing e(theta)=e^(2piitheta), (2) a notation ...

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 ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...