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A285871 Decimal expansion of 1/sqrt(2 - sqrt(2)) (reciprocal of A101464). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
REFERENCES
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10001 [offset adapted to 1 by Georg Fischer, Sep 03 2020]
Eric Weisstein's World of Mathematics, Octagon.
Wikipedia, Octagon.
FORMULA
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
EXAMPLE
1.30656296487637652785664317342718715358376118834926952754889836690808104146...
MAPLE
evalf((sqrt(2-sqrt(2)))^(-1), 100); # Muniru A Asiru, Oct 11 2018
MATHEMATICA
RealDigits[1/Sqrt[2 - Sqrt[2]], 10, 100][[1]] (* Indranil Ghosh, May 11 2017 *)
PROG
(Python)
from sympy import N, sqrt
print(N(1/sqrt(2 - sqrt(2)), 100)) # Indranil Ghosh, May 11 2017
(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
CROSSREFS
Sequence in context: A109693 A188858 A199610 * A322579 A004606 A019808
KEYWORD
nonn,cons,easy
AUTHOR
Wolfdieter Lang, May 11 2017
EXTENSIONS
Offset and example corrected by Amiram Eldar, Aug 07 2020
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)