

A174968


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


14



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



EXAMPLE

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


MATHEMATICA



PROG



CROSSREFS

Cf. A002193 (decimal expansion of sqrt(2)), A010685 (continued fraction expansion of (1 + sqrt(2))/2), A249403.


KEYWORD



AUTHOR



STATUS

approved



