Search Results for ""

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

The shah function is defined by m(x) = sum_(n=-infty)^(infty)delta(x-n) (1) = sum_(n=-infty)^(infty)delta(x+n), (2) where delta(x) is the delta function, so m(x)=0 for x not ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

A constant-curvature surface which can be given parametrically by x = rcosphi (1) y = rsinphi (2) z = (ln[tan(1/2v)]+a(C+1)cosv)/(sqrt(C)), (3) where phi = ...

Given the left factorial function Sigma(n)=sum_(k=1)^nk!, SK(p) for p prime is the smallest integer n such that p|1+Sigma(n-1). The first few known values of SK(p) are 2, 4, ...

If a random variable X has a chi-squared distribution with m degrees of freedom (chi_m^2) and a random variable Y has a chi-squared distribution with n degrees of freedom ...

The compound of the snub cube and its dual, the pentagonal icositetrahedron. Surprisingly, the tribonacci constant t is intimately related to the metric properties of the ...

Borwein et al. (2004, pp. 4 and 44) term the expression of the integrals I_1 = int_0^1x^xdx (1) = 0.783430510... (2) I_2 = int_0^1(dx)/(x^x) (3) = 1.291285997... (4) (OEIS ...

A species of structures is a rule F which 1. Produces, for each finite set U, a finite set F[U], 2. Produces, for each bijection sigma:U->V, a function F[sigma]:F[U]->F[V]. ...

Define the notation [n]f_0=f_(-(n-1)/2)+...+f_0+...+f_((n-1)/2) (1) and let delta be the central difference, so delta^2f_0=f_1-2f_0+f_(-1). (2) Spencer's 21-term moving ...