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A335959
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)).
3
2, 0, 6, 0, 9, 2, 1, 0, 8, 2, 7, 1, 2, 7, 0, 1, 0, 6, 5, 0, 3, 3, 9, 7, 7, 4, 2, 7, 8, 6, 1, 7, 2, 1, 2, 9, 5, 4, 1, 9, 9, 7, 1, 9, 2, 2, 3, 5, 7, 4, 6, 5, 0, 0, 5, 8, 1, 0, 4, 0, 9, 2, 0, 4, 4, 9, 7, 6, 7, 3, 7, 1, 6, 4, 0, 2, 2, 4, 6, 2, 9, 0, 8, 3, 3, 5
OFFSET
0,1
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 *)
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 03 2020
STATUS
approved