This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333202 #18 Sep 02 2024 10:55:44 %S A333202 1,4,7,8,9,4,2,8,5,7,5,4,4,5,9,7,4,3,3,8,2,7,9,0,6,0,1,9,4,3,3,9,1,4, %T A333202 4,3,5,0,7,1,6,9,7,4,3,0,5,9,5,0,0,8,2,5,1,8,8,1,2,1,2,2,4,9,3,3,5,3, %U A333202 8,3,3,6,3,5,2,5,0,6,8,7,8,0,5,1,6,2 %N A333202 Decimal expansion of arclength from (0,0) to (1,1) on y = x^2. %H A333202 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A333202 arclength = (2 sqrt(5) + arcsinh(2))/4. %F A333202 arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4. %e A333202 Equals 1.478942857544597433827906... %t A333202 s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}] %t A333202 r = N[s, 200] %t A333202 RealDigits[r][[1]] %o A333202 (PARI) sqrt(5)/2 + asinh(2)/4 \\ _Charles R Greathouse IV_, Sep 02 2024 %Y A333202 Cf. A333203, A333204, A335996. %K A333202 nonn,cons,easy %O A333202 1,2 %A A333202 _Clark Kimberling_, May 13 2020