

A174968


Decimal expansion of (1 + sqrt(2))/2.


13



1, 2, 0, 7, 1, 0, 6, 7, 8, 1, 1, 8, 6, 5, 4, 7, 5, 2, 4, 4, 0, 0, 8, 4, 4, 3, 6, 2, 1, 0, 4, 8, 4, 9, 0, 3, 9, 2, 8, 4, 8, 3, 5, 9, 3, 7, 6, 8, 8, 4, 7, 4, 0, 3, 6, 5, 8, 8, 3, 3, 9, 8, 6, 8, 9, 9, 5, 3, 6, 6, 2, 3, 9, 2, 3, 1, 0, 5, 3, 5, 1, 9, 4, 2, 5, 1, 9, 3, 7, 6, 7, 1, 6, 3, 8, 2, 0, 7, 8, 6, 3, 6, 7, 5, 0
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OFFSET

1,2


COMMENTS

a(n) is the diameter of the circle around the Vitruvian Man when the square has sides of unit length. See illustration in links.  Kival Ngaokrajang, Jan 29 2015
The iterated function z^2  1/4, starting from z = 0, gives a pretty good rational approximation of (1)((1 + sqrt(2))/2  1) to more than eight decimal digits after just twenty steps.  Alonso del Arte, Apr 09 2016


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Kival Ngaokrajang, Illustration of Vitruvian Man and construction rule
Wikipedia, Vitruvian Man


EXAMPLE

(1 + sqrt(2))/2 = 1.20710678118654752440...


MATHEMATICA

First@RealDigits[(1 + Sqrt[2])/2, 10, 105] (* Michael De Vlieger, Jan 29 2015 *)


PROG

(PARI) (1+sqrt(2))/2 \\ Altug Alkan, Apr 16 2016


CROSSREFS

Cf. A002193 (decimal expansion of sqrt(2)), A010685 (continued fraction expansion of (1 + sqrt(2))/2), A249403.
Sequence in context: A192496 A156442 A268683 * A254445 A346670 A140663
Adjacent sequences: A174965 A174966 A174967 * A174969 A174970 A174971


KEYWORD

cons,nonn,easy


AUTHOR

Klaus Brockhaus, Apr 02 2010


STATUS

approved



