%I #38 Oct 19 2023 16:23:31
%S 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,
%T 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,
%U 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
%N Decimal expansion of the perimeter of Cairo and Prismatic tiles.
%C An algebraic integer with degree 4 and minimal polynomial x^4 - 16x^2 + 16. - _Charles R Greathouse IV_, Apr 21 2016
%C Length of the longest diagonal in a regular 12-gon with unit side. - _Mohammed Yaseen_, Dec 13 2020
%H Paolo Xausa, <a href="/A214726/b214726.txt">Table of n, a(n) for n = 1..10000</a>
%H Ping Ngai Chung, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira and Elena Wikner, <a href="https://www.ams.org/journals/notices/201205/rtx120500632p.pdf">Isoperimetric Pentagonal Tilings</a>, Not. AMS, Vol. 59, No. 5 (May 2012) pp. 632-640; <a href="https://arxiv.org/abs/1111.6161">arXiv preprint</a>, arXiv:1111.6161 [math.MG], 2011.
%F Equals 2*(sqrt(2+sqrt(3))).
%F Equals csc(Pi/12). - _Amiram Eldar_, May 28 2021
%F Equals sqrt(2) + sqrt(6). - _Vaclav Kotesovec_, May 28 2021
%e 3.8637033051562731469989727989....
%t First[RealDigits[Csc[Pi/12],10,100]] (* _Paolo Xausa_, Oct 19 2023 *)
%o (PARI) 2*sqrt(2+sqrt(3)) \\ _Charles R Greathouse IV_, Apr 21 2016
%Y Cf. A002193, A002194.
%K nonn,cons,easy
%O 1,1
%A _Jonathan Vos Post_, Jul 26 2012
%E a(100) corrected by _Georg Fischer_, Jul 12 2021
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