What is 0.25801227546?

Question

Due to specific knowledge, I know that this is a constant which has a very nice closed form expression (probably short and in terms of square roots, rationals, and $\pi$). However, the Inverse Symbolic Calculator and I can't find it. What is $0.25801227546$ a very good approximation to?

Answer 1

I used the program $\texttt{ries}$ and it found a close match:

> ries 0.25801227546

   Your target value: T = 0.25801227546                          mrob.com/ries

               cospi(x) = ln(2)                  for x = T - 0.00178869  {54}
                e^(1/x) = 7^2                    for x = T - 0.0010631   {62}
                   3"/x = 2/pi                   for x = T + 5.59597e-12 {69}
                  (for more results, use the option '-l3')

  ln(x) = natural logarithm or log base e  cospi(X) = cos(pi * x)
  A"/B = Ath root of B  pi = 3.14159...

which gives the value $(2/\pi)^3$.