A335958 - OEIS

%I #4 Jul 04 2020 01:45:30

%S 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 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 5,0,2,9,9,0,2,9,4,1,5,5,0,6,4,5,1,0

%N 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 s/c = 1.24189118251777949328029742670369236529...

%e c/s = 0.80522352849999684548520974994993752239...

%e c-s = 0.20609210827127010650339774278617212954...

%t r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]

%t r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]

%t r1/r2

%t r2/r1

%t r1 - r2

%t RealDigits[r1/r2][[1]]      (* A335957 *)

%t RealDigits[r2/r1][[1]]      (* A335958 *)

%t RealDigits[r1 - r2][[1]]    (* A335959 *)

%Y Cf. A335928, A335929, A335930, A335931, A335932, A335957, A335959.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 03 2020