A336078 -id:A336078 - cp's OEIS frontend

A336073 Decimal expansion of the ratio of segment areas for arclength 1/3 on the unit circle; see Comments.

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

Offset: 4

Clark Kimberling, Jul 10 2020

Suppose that s in (0,Pi) is the length of an arc of the unit circle.  The associated chord separates the interior into two segments. Let A1 be the area of the larger and A2 the area of the smaller. The term "ratio of segment areas" means A1/A2.
*****************
Guide to related sequences:
arclength,s   ratio, A1/A2
1/3           A336073
Pi/6          A336074
Pi/5          A336075
Pi/4          A336076
Pi/3          A336077
Pi/2          A336078
1             A336079
2             A336080
3             A336081
*****************
ratio, A1/A2  arclength, s
2             A336082
3             A336083
4             A336084
5             A336085
1/2           A336086

			ratio = 1022.54737393604920361975925805839994393435790826122033281

Cf. A336059-A336086.

s = 1/3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
RealDigits[r][[1]]

2*Pi/(1/3 - sin(1/3)) - 1 \\ Charles R Greathouse IV, Feb 22 2025

ratio = (2*Pi - s + sin(s))/(s - sin(s)), where s = 1/3.

cp's OEIS Frontend

A336073 Decimal expansion of the ratio of segment areas for arclength 1/3 on the unit circle; see Comments.

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