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A336043 Decimal expansion of the solution s of s/c = 3/2, where s = arclength and c = chord length on the unit circle. 15
2, 9, 9, 1, 5, 6, 3, 1, 3, 6, 4, 4, 4, 1, 9, 9, 4, 2, 0, 4, 3, 0, 9, 8, 7, 6, 9, 9, 1, 5, 1, 9, 1, 9, 4, 3, 1, 3, 4, 1, 3, 4, 9, 4, 1, 4, 2, 0, 7, 8, 6, 9, 3, 0, 1, 7, 1, 5, 5, 8, 3, 0, 1, 9, 4, 8, 2, 0, 9, 3, 1, 6, 4, 7, 9, 9, 2, 7, 9, 4, 6, 7, 2, 1, 5, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For every constant k > 1, the ratio s/c such that s/c = k is the same for all circles.  Choosing the unit circle, x^2 + y^2 = 1, we have c = sqrt(2 - 2*cos(s)), so that the solution of s/c = k is the solution of s = k*sqrt(2 - 2*cos(s)).  For each s in (0, 2*Pi) there is a unique solution c; for each c in (0, Pi), there are two solutions s; if one of them is s_0, the other is 2*Pi - s_0.

Guide to related sequences:

  ratio, s/c     arclength, s    chord length, c

  3/2            A336043         A336044

  2              A336045         A199460

  3              A336047         A336048

  Pi             A336049         A336050

  4              A336051         A336052

  5              A336053         A336054

  6              A336055         A336056

  2*Pi           A336057         A336058

LINKS

Table of n, a(n) for n=1..86.

FORMULA

s = 2.9915631364441994204309876991519194313413...

c = 1.9943754242961329469539917994346129542275...

MATHEMATICA

t = t /.FindRoot[t == (3/2) Sqrt[2 - 2 Cos[t]], {t, 4}, WorkingPrecision -> 200]

c = 2 t/3

RealDigits[t][[1]]   (* A336043 *)

RealDigits[c][[1]]   (* A336044 *)

CROSSREFS

Cf. A336044.

Sequence in context: A011072 A175295 A198141 * A340723 A201765 A160331

Adjacent sequences:  A336040 A336041 A336042 * A336044 A336045 A336046

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jul 06 2020

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)