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A090388 Decimal expansion of 1 + sqrt(3).

%I A090388 #61 Aug 04 2025 08:56:41
%S A090388 2,7,3,2,0,5,0,8,0,7,5,6,8,8,7,7,2,9,3,5,2,7,4,4,6,3,4,1,5,0,5,8,7,2,
%T A090388 3,6,6,9,4,2,8,0,5,2,5,3,8,1,0,3,8,0,6,2,8,0,5,5,8,0,6,9,7,9,4,5,1,9,
%U A090388 3,3,0,1,6,9,0,8,8,0,0,0,3,7,0,8,1,1,4,6,1,8,6,7,5,7,2,4,8,5,7,5,6
%N A090388 Decimal expansion of 1 + sqrt(3).
%C A090388 1 + sqrt(3) is the length of the minimal Steiner network that connects the four vertices of a unit square. - _Lekraj Beedassy_, May 02 2008
%C A090388 This is the case n = 12 in the identity (Gamma(1/n)/Gamma(3/n))*(Gamma((n-1)/n)/Gamma((n-3)/n)) = 1 + 2*cos(2*Pi/n). - _Bruno Berselli_, Dec 14 2012
%C A090388 Equals n + n/(n + n/(n + n/(n + ...))) for n = 2. - _Stanislav Sykora_, Jan 23 2014
%C A090388 A non-optimal solution to the problem of finding the length of shortest fence that protects privacy of a square garden [Kawohl]. Cf. A256965. - _N. J. A. Sloane_, Apr 14 2015
%C A090388 Perimeter of a 30-60-90 triangle with longest leg equal to 1. - _Wesley Ivan Hurt_, Apr 09 2016
%C A090388 Length of the second shortest diagonal in a regular 12-gon with unit side. - _Mohammed Yaseen_, Dec 13 2020
%C A090388 Surface area of a square pyramid (Johnson solid J_1) with unit edges. - _Paolo Xausa_, Aug 04 2025
%H A090388 G. C. Greubel, <a href="/A090388/b090388.txt">Table of n, a(n) for n = 1..10000</a>
%H A090388 Bernd Kawohl, <a href="http://www.mi.uni-koeln.de/mi/Forschung/Kawohl/kawohl/springercime.ps">Some nonconvex shape optimization problems, in: Optimal Shape Design</a>, Eds. A.Cellina u. A. Ornelas, Springer Lecture Notes in Math.1740 (2000), p. 7-46.
%H A090388 Ian Stewart, <a href="http://www.mi.uni-koeln.de/mi/Forschung/Kawohl/various/Bilder/PolygonalPrivacy.pdf">Pursuing Polygonal Privacy</a>, Mathematical Recreations Column, Scientific American, 284 (No. 2, 2001), 88-89.
%H A090388 Wikipedia, <a href="https://en.wikipedia.org/wiki/Square_pyramid">Square pyramid</a>.
%H A090388 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A090388 Equals 1 + A002194. - _R. J. Mathar_, Oct 16 2015
%F A090388 Equals A019973 -1 . - _R. J. Mathar_, May 25 2023
%e A090388 2.7320508075688772...
%p A090388 Digits:=100: evalf((1+sqrt(3))); # _Wesley Ivan Hurt_, Apr 09 2016
%t A090388 RealDigits[1 + Sqrt[3], 10, 100][[1]] (* _Alonso del Arte_, Feb 23 2014 *)
%o A090388 (PARI) 1 + sqrt(3) \\ _Michel Marcus_, Apr 10 2016
%Y A090388 Cf. n + n/(n + n/(n + ...)): A090458 (n = 3), A090488 (n = 4), A090550 (n = 5), A092294 (n = 6), A092290 (n = 7), A090654 (n = 8), A090655 (n = 9), A090656 (n = 10). - _Stanislav Sykora_, Jan 23 2014
%Y A090388 Cf., also A256965.
%K A090388 easy,nonn,cons
%O A090388 1,1
%A A090388 _Felix Tubiana_, Feb 05 2004
%E A090388 Better definition from _Rick L. Shepherd_, Jul 02 2004