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

4,3

Comments

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

Links

Table of n, a(n) for n=4..89.

Formula

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

Example

ratio = 1022.54737393604920361975925805839994393435790826122033281

Mathematica

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

Crossrefs

Cf. A336059-A336086.

Sequence in context: A261114 A284827 A241306 * A266792 A162200 A290289

Adjacent sequences: A336070 A336071 A336072 * A336074 A336075 A336076

Keyword

nonn,cons

Author

Clark Kimberling, Jul 10 2020

Status

approved