

A336083


Decimal expansion of the arclength on the unit circle such that the corresponding chord separates the interior into segments having 3 = ratio of segment areas; see Comments.


1



2, 3, 0, 9, 8, 8, 1, 4, 6, 0, 0, 1, 0, 0, 5, 7, 2, 6, 0, 8, 8, 6, 6, 3, 3, 7, 7, 9, 3, 1, 3, 6, 2, 4, 8, 4, 6, 1, 1, 1, 9, 9, 6, 4, 5, 8, 5, 8, 8, 3, 1, 0, 3, 7, 5, 4, 5, 3, 1, 5, 2, 9, 3, 1, 9, 2, 7, 1, 9, 2, 8, 5, 8, 0, 2, 6, 6, 5, 2, 0, 9, 3, 9, 1, 3, 3
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



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.


FORMULA

Equals d+Pi/2 = A003957 + A019669, where d is the Dottie number.  Gleb Koloskov, Feb 21 2021


EXAMPLE

arclength = 2.3098814600100572608866337793136248461119964...


MATHEMATICA

k = 3; s = s /. FindRoot[(2 Pi  s + Sin[s])/(s  Sin[s]) == k, {s, 2}, WorkingPrecision > 200]
RealDigits[s][[1]]


PROG

(PARI) d=solve(x=0, 1, cos(x)x); d+Pi/2 \\ Gleb Koloskov, Feb 21 2021


CROSSREFS

Cf. A336073, A003957, A019669.
Sequence in context: A098989 A175315 A180186 * A256294 A279412 A012399
Adjacent sequences: A336080 A336081 A336082 * A336084 A336085 A336086


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Jul 11 2020


STATUS

approved



