A336079 Decimal expansion of the ratio of segment areas for arclength 1 on the unit circle; see Comments.

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

Offset

2,1

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. See A336073 for a guide to related sequences.

Links

Table of n, a(n) for n=2..87.

Formula

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

Example

ratio = 38.63429218030340056508641778759493689126124881320...

Mathematica

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

Crossrefs

Cf. A336073.

Sequence in context: A016627 A175184 A019604 * A214726 A106291 A137987

Adjacent sequences: A336076 A336077 A336078 * A336080 A336081 A336082

Keyword

nonn,cons

Author

Clark Kimberling, Jul 11 2020

Status

approved