A336086 Decimal expansion of the arclength on the unit circle such that the corresponding chord separates the interior into segments having 1/2 = ratio of segment areas; see Comments.

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

Offset

1,1

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=1..86.

Example

arclength = 3.6778596325786837912250924511460299669533...

Mathematica

k = 1/2; s = s /. FindRoot[(2 Pi - s + Sin[s])/(s - Sin[s]) == k, {s, 2}, WorkingPrecision -> 200]
RealDigits[s][[1]]

Crossrefs

Cf. A336073.

Sequence in context: A067753 A129023 A188883 * A152083 A251532 A251533

Adjacent sequences: A336083 A336084 A336085 * A336087 A336088 A336089

Keyword

nonn,cons

Author

Clark Kimberling, Jul 11 2020

Status

approved