OFFSET
1,2
FORMULA
arclength = (2 sqrt(5) + arcsinh(2))/4.
arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4.
EXAMPLE
Equals 1.478942857544597433827906...
MATHEMATICA
s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]
PROG
(PARI) sqrt(5)/2 + asinh(2)/4 \\ Charles R Greathouse IV, Sep 02 2024
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, May 13 2020
STATUS
approved