A285871 - OEIS

%I #37 May 31 2024 20:41:53

%S 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 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 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 Decimal expansion of 1/sqrt(2 - sqrt(2)) (reciprocal of A101464).

%C This number is the length ratio of the radius of a circle and the side of the inscribed octagon.

%C 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 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Octagon.html">Octagon</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Octagon">Octagon</a>.

%F Equals 1/(2*sin(Pi/8)) = 1/A101464.

%F Equals Product_{k>=0} (1 + (-1)^k/(4*k+2)). - _Amiram Eldar_, Aug 07 2020

%F The minimal polynomial is 2*x^4 - 4*x^2 + 1. - _Joerg Arndt_, May 10 2021

%e 1.30656296487637652785664317342718715358376118834926952754889836690808104146...

%p evalf((sqrt(2-sqrt(2)))^(-1),100); # _Muniru A Asiru_, Oct 11 2018

%t RealDigits[1/Sqrt[2 - Sqrt[2]], 10, 100][[1]] (* _Indranil Ghosh_, May 11 2017 *)

%o (Python)

%o from sympy import N, sqrt

%o print(N(1/sqrt(2 - sqrt(2)), 100)) # _Indranil Ghosh_, May 11 2017

%o (PARI) default(realprecision, 100); 1/sqrt(2 - sqrt(2)) \\ _G. C. Greubel_, Oct 10 2018

%o (Magma) SetDefaultRealField(RealField(100)); 1/Sqrt(2 - Sqrt(2)); // _G. C. Greubel_, Oct 10 2018

%Y Cf. A101464, A179260.

%K nonn,cons,easy

%O 1,2

%A _Wolfdieter Lang_, May 11 2017

%E Offset and example corrected by _Amiram Eldar_, Aug 07 2020