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

Author

Jonathan Vos Post, Jul 26 2012

Keywords

• nonn
• cons
• easy

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

Examples

			3.8637033051562731469989727989....
		

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.

Crossrefs

Cf. A002193, A002194, A019884.

Programs

Mathematica

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

PARI

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

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

Extensions

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