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A337402 Decimal expansion of the length of third shortest diagonal in a regular 12-gon with unit edge length. 1
3, 3, 4, 6, 0, 6, 5, 2, 1, 4, 9, 5, 1, 2, 3, 1, 6, 2, 2, 3, 0, 1, 1, 7, 5, 1, 2, 3, 6, 6, 7, 4, 9, 2, 8, 1, 3, 8, 3, 7, 4, 8, 1, 5, 5, 3, 3, 9, 3, 7, 5, 7, 1, 7, 3, 9, 8, 1, 3, 6, 5, 8, 9, 0, 6, 1, 1, 5, 7, 8, 9, 0, 6, 4, 2, 1, 8, 1, 8, 0, 7, 1, 5, 4, 5, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The distinct diagonal lengths in a regular 12-gon ABC...JKL with unit edge length are

AC = sqrt(2 +   sqrt(3)) =     sqrt(2)/(-1+sqrt(3)) = A188887

AD = sqrt(4 + 2*sqrt(3)) =          2 /(-1+sqrt(3)) = A090388

AE = sqrt(6 + 3*sqrt(3)) =     sqrt(6)/(-1+sqrt(3))

AF = sqrt(7 + 4*sqrt(3)) = (1+sqrt(3))/(-1+sqrt(3)) = A019973

AG = sqrt(8 + 4*sqrt(3)) =   2*sqrt(2)/(-1+sqrt(3)) = A214726

LINKS

Table of n, a(n) for n=1..87.

FORMULA

Equals sin(Pi/3)/sin(Pi/12) = sqrt(2) + 2*cos(Pi/12) = sqrt(3*cot(Pi/12)).

Equals sqrt(6 + 3*sqrt(3)) = sqrt(6)/(-1+sqrt(3)) = (3+sqrt(3))/(sqrt(2).

Equals 3*A145439.

EXAMPLE

3.34606521495123162230117512366749281383748155339375...

PROG

(PARI) sqrt(6 + 3*sqrt(3)) \\ Michel Marcus, Aug 26 2020

CROSSREFS

Cf. A337301, A188887, A090388, A019973, A214726, A145439.

Sequence in context: A241442 A043551 A162888 * A151759 A008443 A196456

Adjacent sequences:  A337399 A337400 A337401 * A337403 A337404 A337405

KEYWORD

nonn,cons

AUTHOR

Mohammed Yaseen, Aug 26 2020

STATUS

approved

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Last modified October 17 17:21 EDT 2021. Contains 348065 sequences. (Running on oeis4.)