A214726 Decimal expansion of the perimeter of Cairo and Prismatic tiles.

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

Offset

1,1

Comments

An algebraic integer with degree 4 and minimal polynomial x^4 - 16x^2 + 16. - Charles R Greathouse IV, Apr 21 2016

Length of the longest diagonal in a regular 12-gon with unit side. - Mohammed Yaseen, Dec 13 2020

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Ping Ngai Chung, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira, and Elena Wikner, Isoperimetric Pentagonal Tilings, Not. AMS, Vol. 59, No. 5 (May 2012) pp. 632-640; arXiv preprint, arXiv:1111.6161 [math.MG], 2011.

Formula

Equals 2*(sqrt(2+sqrt(3))).

Equals csc(Pi/12). - Amiram Eldar, May 28 2021

Equals sqrt(2) + sqrt(6). - Vaclav Kotesovec, May 28 2021

Equals Product_{k>=1} (25 - 144*k^2)/(100 - 144*k^2). - Antonio Graciá Llorente, Jul 13 2024

Equals 4 * A019884. - Alois P. Heinz, Jul 14 2024

Example

3.8637033051562731469989727989....

Mathematica

First[RealDigits[Csc[Pi/12], 10, 100]] (* Paolo Xausa, Oct 19 2023 *)

Prog

(PARI) 2*sqrt(2+sqrt(3)) \\ Charles R Greathouse IV, Apr 21 2016

Crossrefs

Cf. A002193, A002194, A019884.

Sequence in context: A175184 A019604 A336079 * A106291 A137987 A212007

Adjacent sequences: A214723 A214724 A214725 * A214727 A214728 A214729

Keyword

nonn,cons,easy

Author

Jonathan Vos Post, Jul 26 2012

Extensions

a(100) corrected by Georg Fischer, Jul 12 2021

Status

approved