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)).

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

Offset: 0

Author

Clark Kimberling, Jul 03 2020

Keywords

• nonn
• cons

Examples

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

Crossrefs

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

Programs

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 *)