Search Results for ""

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

136·2^(256) approx 1.575×10^(79). According to Eddington, the exact number of protons in the universe, where 136 was the reciprocal of the fine structure constant as best as ...

The bias of a series is defined as Q[a_i,a_(i+1),a_(i+2)]=(a_ia_(i+2)-a_(i+1)^2)/(a_ia_(i+1)a_(i+2)). A series is geometric iff Q=0. A series is artistic iff the bias is ...

The coordinate system obtained by inversion of Cartesian coordinates, with u,v,w in (-infty,infty). The transformation equations are x = u/(u^2+v^2+w^2) (1) y = ...

A coordinate system which is similar to bispherical coordinates but having fourth-degree surfaces instead of second-degree surfaces for constant mu. The coordinates are given ...

Landau (1911) proved that for any fixed x>1, sum_(0<|I[rho]|<=T)x^rho=-T/(2pi)Lambda(x)+O(lnT) as T->infty, where the sum runs over the nontrivial Riemann zeta function zeros ...

Binet's formula is an equation which gives the nth Fibonacci number as a difference of positive and negative nth powers of the golden ratio phi. It can be written as F_n = ...

The roulette traced by a point P attached to a circle of radius b rolling around the outside of a fixed circle of radius a. These curves were studied by Dürer (1525), ...

The Rayleigh functions sigma_n(nu) for n=1, 2, ..., are defined as sigma_n(nu)=sum_(k=1)^inftyj_(nu,k)^(-2n), where +/-j_(nu,k) are the zeros of the Bessel function of the ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...