cp's OEIS Frontend

A335958 Decimal expansion of c/s, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

%I A335958 #4 Jul 04 2020 01:45:30
%S A335958 8,0,5,2,2,3,5,2,8,4,9,9,9,9,6,8,4,5,4,8,5,2,0,9,7,4,9,9,4,9,9,3,7,5,
%T A335958 2,2,3,9,4,1,7,1,6,9,9,6,9,8,5,2,2,2,1,0,2,8,1,2,4,7,1,7,9,5,2,6,4,7,
%U A335958 5,0,2,9,9,0,2,9,4,1,5,5,0,6,4,5,1,0
%N A335958 Decimal expansion of c/s, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).
%e A335958 s/c = 1.24189118251777949328029742670369236529...
%e A335958 c/s = 0.80522352849999684548520974994993752239...
%e A335958 c-s = 0.20609210827127010650339774278617212954...
%t A335958 r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
%t A335958 r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
%t A335958 r1/r2
%t A335958 r2/r1
%t A335958 r1 - r2
%t A335958 RealDigits[r1/r2][[1]]      (* A335957 *)
%t A335958 RealDigits[r2/r1][[1]]      (* A335958 *)
%t A335958 RealDigits[r1 - r2][[1]]    (* A335959 *)
%Y A335958 Cf. A335928, A335929, A335930, A335931, A335932, A335957, A335959.
%K A335958 nonn,cons
%O A335958 0,1
%A A335958 _Clark Kimberling_, Jul 03 2020