A336074 Decimal expansion of the ratio of segment areas for arclength Pi/6 on the unit circle; see Comments.

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

Offset

3,1

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=3..88.

Formula

ratio = (2*Pi - s + sin(s))/(s - sin(s)), where s = Pi/6.

Example

ratio = 265.25047901351764771254818549254008953843516090523...

Mathematica

s = Pi/6; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
RealDigits[r][[1]]

Crossrefs

Cf. A336073.

Sequence in context: A271533 A335995 A304585 * A021381 A323501 A157890

Adjacent sequences: A336071 A336072 A336073 * A336075 A336076 A336077

Keyword

nonn,cons

Author

Clark Kimberling, Jul 10 2020

Status

approved