This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A174968 #51 Aug 29 2025 15:39:36
%S A174968 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,
%T A174968 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,
%U A174968 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
%N A174968 Decimal expansion of (1 + sqrt(2))/2.
%C A174968 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
%C A174968 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
%C A174968 This sequence describes the minimum Euclidean length of the optimal solution of the well-known Nine dots puzzle, published in Sam Loyd’s Cyclopedia of puzzles (1914), p. 301 since a valid polygonal chain satisfying the conditions of the above-mentioned problem is (0, 1)-(0, 3)-(3, 0)-(0, 0)-(2, 2), and its total length is equal to 5*(1 + sqrt(2)) = 12.071... (i.e., 10*(1 + sqrt(2))/2). - _Marco Ripà_, Jul 22 2024
%H A174968 G. C. Greubel, <a href="/A174968/b174968.txt">Table of n, a(n) for n = 1..10000</a>
%H A174968 Kival Ngaokrajang, <a href="/A174968/a174968_4.pdf">Illustration of Vitruvian Man and construction rule</a>.
%H A174968 Marco Ripà, <a href="https://arxiv.org/abs/2207.08708">Shortest polygonal chains covering each planar square grid</a>, arXiv:2207.08708v3 [math.CO], 2024.
%H A174968 Wikipedia, <a href="http://en.wikipedia.org/wiki/Vitruvian_Man">Vitruvian Man</a>.
%H A174968 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A174968 Equals Product_{k>=2} (1 + (-1)^k/A079291(k)). - _Amiram Eldar_, Dec 03 2024
%e A174968 1.20710678118654752440084436210484903928483593768847...
%t A174968 First@RealDigits[(1 + Sqrt[2])/2, 10, 105] (* _Michael De Vlieger_, Jan 29 2015 *)
%o A174968 (PARI) (1+sqrt(2))/2 \\ _Altug Alkan_, Apr 16 2016
%Y A174968 Cf. A002193 (decimal expansion of sqrt(2)), A010685 (continued fraction expansion of (1 + sqrt(2))/2), A079291, A249403.
%Y A174968 Apart from initial digits the same as A157214 and A010503.
%K A174968 cons,nonn,easy,changed
%O A174968 1,2
%A A174968 _Klaus Brockhaus_, Apr 02 2010