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A285871
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Decimal expansion of 1/sqrt(2 - sqrt(2)) (reciprocal of A101464).
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1
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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, 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, 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
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OFFSET
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1,2
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COMMENTS
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This number is the length ratio of the radius of a circle and the side of the inscribed octagon.
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.
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Octagon.
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FORMULA
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Equals 1/(2*sin(Pi/8)) = 1/A101464.
Equals Product_{k>=0} (1 + (-1)^k/(4*k+2)). - Amiram Eldar, Aug 07 2020
The minimal polynomial is 2*x^4 - 4*x^2 + 1. - Joerg Arndt, May 10 2021
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EXAMPLE
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1.30656296487637652785664317342718715358376118834926952754889836690808104146...
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MAPLE
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MATHEMATICA
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RealDigits[1/Sqrt[2 - Sqrt[2]], 10, 100][[1]] (* Indranil Ghosh, May 11 2017 *)
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PROG
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(Python)
from sympy import N, sqrt
(PARI) default(realprecision, 100); 1/sqrt(2 - sqrt(2)) \\ G. C. Greubel, Oct 10 2018
(Magma) SetDefaultRealField(RealField(100)); 1/Sqrt(2 - Sqrt(2)); // G. C. Greubel, Oct 10 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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