Search Results for ""

A subfield which is strictly smaller than the field in which it is contained. The field of rationals Q is a proper subfield of the field of real numbers R which, in turn, is ...

A Stoneham number is a number alpha_(b,c) of the form alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k), where b,c>1 are relatively prime positive integers. Stoneham (1973) proved ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

The hyperbolic cosine integral, often called the "Chi function" for short, is defined by Chi(z)=gamma+lnz+int_0^z(cosht-1)/tdt, (1) where gamma is the Euler-Mascheroni ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...

Wolfram's iteration is an algorithm for computing the square root of a rational number 1<=r<4 using properties of the binary representation of r. The algorithm begins with ...

Van der Corput's constant is given by m = 2sqrt(2)int_0^(sqrt(pi/2-c))cos(x^2+c)dx (1) = 2pi[coscC(phi)-sincS(phi)] (2) = 3.3643175781... (3) (OEIS A143305), where C(x) and ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).