A335957 Decimal expansion of s/c, 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)).

1, 2, 4, 1, 8, 9, 1, 1, 8, 2, 5, 1, 7, 7, 7, 9, 4, 9, 3, 2, 8, 0, 2, 9, 7, 4, 2, 6, 7, 0, 3, 6, 9, 2, 3, 6, 5, 2, 9, 6, 2, 9, 4, 7, 6, 4, 2, 5, 6, 1, 6, 6, 2, 1, 3, 8, 6, 4, 8, 0, 3, 3, 4, 7, 0, 3, 7, 1, 8, 8, 4, 7, 4, 9, 7, 8, 7, 6, 5, 8, 2, 8, 2, 5, 8, 0

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Example

s/c = 1.24189118251777949328029742670369236529...
c/s = 0.80522352849999684548520974994993752239...
c-s = 0.20609210827127010650339774278617212954...

Mathematica

r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
r1/r2
r2/r1
r1 - r2
RealDigits[r1/r2][[1]]      (* A335957 *)
RealDigits[r2/r1][[1]]      (* A335958 *)
RealDigits[r1 - r2][[1]]    (* A335959 *)

Crossrefs

Cf. A335928, A335929, A335930, A335931, A335932, A335958, A335959.

Sequence in context: A254179 A328641 A208741 * A057115 A065276 A065288

Adjacent sequences: A335954 A335955 A335956 * A335958 A335959 A335960

Keyword

nonn,cons

Author

Clark Kimberling, Jul 03 2020

Status

approved