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A020837 Decimal expansion of 1/sqrt(80) = sqrt(5)/20.

%I A020837 #47 Oct 19 2024 15:57:32
%S A020837 1,1,1,8,0,3,3,9,8,8,7,4,9,8,9,4,8,4,8,2,0,4,5,8,6,8,3,4,3,6,5,6,3,8,
%T A020837 1,1,7,7,2,0,3,0,9,1,7,9,8,0,5,7,6,2,8,6,2,1,3,5,4,4,8,6,2,2,7,0,5,2,
%U A020837 6,0,4,6,2,8,1,8,9,0,2,4,4,9,7,0,7,2,0,7,2,0,4,1,8,9,3,9,1,1,3
%N A020837 Decimal expansion of 1/sqrt(80) = sqrt(5)/20.
%C A020837 Multiplied by 100, this is sqrt(125). - _Alonso del Arte_, Jan 06 2013
%C A020837 Multiplied by 10, this is sqrt(5)/2. As such, it appears in the Pythagorean tree as the ratio of the distance between 2 consecutive square centers divided by the length of the initial square (see CNRS link). - _Michel Marcus_, Feb 20 2013
%C A020837 The two-dimensional Steinitz constant K_2(0,0), related to sum of vectors, is sqrt(5)/2. - _Jean-François Alcover_, Jun 04 2014
%C A020837 sqrt(5)/2 is the length of the shortest line segment needed to dissect the unit square into 4 regions with equal areas if all the line segments start at the same vertex of the square. - _Wesley Ivan Hurt_, May 18 2021
%C A020837 sqrt(5)/2 is the standard deviation of rolling a 4-sided die. - _Mohammed Yaseen_, Feb 23 2023
%D A020837 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.13 Steinitz constants, p. 241.
%H A020837 Ivan Panchenko, <a href="/A020837/b020837.txt">Table of n, a(n) for n = 0..1000</a>
%H A020837 Étienne Ghys and Jos Leys, <a href="http://images-archive.math.cnrs.fr/Un-arbre-pythagoricien.html">Un arbre pythagoricien</a> — Images des Mathématiques, CNRS, 2013.
%H A020837 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A020837 Equals 1/sqrt(80) = sqrt(5)/20 = (-1 + 2*phi)/20, with phi from A001622.
%F A020837 Equals 0.1 * Sum_{k>=0} binomial(2*k,k)/20^k. - _Amiram Eldar_, Aug 04 2022
%e A020837 sqrt(5)/20 = 0.111803398874989484820458683436563811772...
%e A020837 sqrt(5)/2  = 1.118033988749894848204586834365638117720...
%t A020837 RealDigits[1/Sqrt[80], 10, 120][[1]] (* _Harvey P. Dale_, May 01 2012 *)
%o A020837 (PARI) sqrt(1/80) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y A020837 c = (1/10)*(A001622 - 1/2) = (1/10)*(7/2 - A079585) = (A176055 - 1)/10.
%K A020837 nonn,easy,cons
%O A020837 0,4
%A A020837 _N. J. A. Sloane_