This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A285871 #43 Feb 16 2025 08:33:44
%S A285871 1,3,0,6,5,6,2,9,6,4,8,7,6,3,7,6,5,2,7,8,5,6,6,4,3,1,7,3,4,2,7,1,8,7,
%T A285871 1,5,3,5,8,3,7,6,1,1,8,8,3,4,9,2,6,9,5,2,7,5,4,8,8,9,8,3,6,6,9,0,8,0,
%U A285871 8,1,0,4,1,4,6,1,1,9,2,0,5,0,9,5,1,8,5,3,7,2,0,1,9,2,6,2,8,1,4
%N A285871 Decimal expansion of 1/sqrt(2 - sqrt(2)) (reciprocal of A101464).
%C A285871 This number is the length ratio of the radius of a circle and the side of the inscribed octagon.
%C A285871 In the Corbalán reference, pp. 61-62, this number is called Cordoba number or Cordoba proportion, attributed to the architect Rafael de la Hoz (1924-2000), who used the rectangle with this proportion to explain the structure of the Mihrab of Cordoba.
%D A285871 Fernando Corbalán, Der goldene Schnitt, Librero, 2017. Original: La proportión áurea, RBA Contenidos Editoriales y Audiovisuales S. A. U., 2010. English: The golden Ratio, 2012, RBA Coleccionables.
%H A285871 G. C. Greubel, <a href="/A285871/b285871.txt">Table of n, a(n) for n = 1..10001</a> [offset adapted to 1 by _Georg Fischer_, Sep 03 2020]
%H A285871 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Octagon.html">Octagon</a>.
%H A285871 Wikipedia, <a href="https://en.wikipedia.org/wiki/Octagon">Octagon</a>.
%H A285871 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A285871 Equals 1/(2*sin(Pi/8)) = 1/A101464.
%F A285871 Equals Product_{k>=0} (1 + (-1)^k/(4*k+2)). - _Amiram Eldar_, Aug 07 2020
%F A285871 The minimal polynomial is 2*x^4 - 4*x^2 + 1. - _Joerg Arndt_, May 10 2021
%F A285871 Equals Sum_{n>=0} binomial(2*n - 1/2, -1/2)/2^n. - _Antonio Graciá Llorente_, Nov 13 2024
%e A285871 1.30656296487637652785664317342718715358376118834926952754889836690808104146...
%p A285871 evalf((sqrt(2-sqrt(2)))^(-1),100); # _Muniru A Asiru_, Oct 11 2018
%t A285871 RealDigits[1/Sqrt[2 - Sqrt[2]], 10, 100][[1]] (* _Indranil Ghosh_, May 11 2017 *)
%o A285871 (Python)
%o A285871 from sympy import N, sqrt
%o A285871 print(N(1/sqrt(2 - sqrt(2)), 100)) # _Indranil Ghosh_, May 11 2017
%o A285871 (PARI) default(realprecision, 100); 1/sqrt(2 - sqrt(2)) \\ _G. C. Greubel_, Oct 10 2018
%o A285871 (Magma) SetDefaultRealField(RealField(100)); 1/Sqrt(2 - Sqrt(2)); // _G. C. Greubel_, Oct 10 2018
%Y A285871 Cf. A101464, A179260.
%K A285871 nonn,cons,easy
%O A285871 1,2
%A A285871 _Wolfdieter Lang_, May 11 2017
%E A285871 Offset and example corrected by _Amiram Eldar_, Aug 07 2020