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 A020829 #63 Aug 04 2025 08:56:54
%S A020829 1,1,7,8,5,1,1,3,0,1,9,7,7,5,7,9,2,0,7,3,3,4,7,4,0,6,0,3,5,0,8,0,8,1,
%T A020829 7,3,2,1,4,1,3,9,3,2,2,9,4,8,0,7,9,0,0,6,0,9,8,0,5,6,6,4,4,8,3,2,5,6,
%U A020829 1,0,3,9,8,7,1,8,4,2,2,5,3,2,3,7,5,3,2,2,9,4,5,2,7,3,0,3,4,6,4
%N A020829 Decimal expansion of 1/sqrt(72) = 1/(3*2^(3/2)) = sqrt(2)/12.
%C A020829 Volume of regular tetrahedron with unit edge. - _Stanislav Sykora_, May 31 2012
%C A020829 In the dragon curve fractal, (5/6)*sqrt(2) = 1.1785.... is the maximum distance of any point from curve start. Such a maximum must be to a vertex of the convex hull. Hull vertices are shown by Benedek and Panzone (theorem 3, page 85) and their P8 = 7/6 - (1/6)i at distance sqrt((7/6)^2 + (1/6)^2) is the maximum. - _Kevin Ryde_, Nov 22 2019
%C A020829 With offset 1, volume of a triangular cupola (Johnson solid J_3) with unit edges. - _Paolo Xausa_, Aug 04 2025
%D A020829 Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 450.
%H A020829 Ivan Panchenko, <a href="/A020829/b020829.txt">Table of n, a(n) for n = 0..1000</a>
%H A020829 Agnes I. Benedek and Rafael Panzone, <a href="https://inmabb.criba.edu.ar/revuma/pdf/v39n1y2/p076-089.pdf">On Some Notable Plane Sets, II: Dragons</a>, Revista de la Unión Matemática Argentina, volume 39, numbers 1-2, 1994, pages 76-90.
%H A020829 Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>.
%H A020829 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>.
%H A020829 Wikipedia, <a href="https://en.wikipedia.org/wiki/Triangular_cupola">Triangular cupola</a>.
%H A020829 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A020829 Equals Integral_{x=0..Pi/4} sin(x)^2 * cos(x) dx. - _Amiram Eldar_, May 31 2021
%F A020829 Equals 1/A010524 = A020765/3 = A020775/2 = A378207/5. - _Hugo Pfoertner_, Jan 26 2025
%e A020829 0.117851130197757920733474...
%t A020829 RealDigits[Sqrt[2]/12, 10, 50][[1]] (* _G. C. Greubel_, Jul 06 2017 *)
%o A020829 (PARI) sqrt(2)/12 \\ _G. C. Greubel_, Jul 06 2017
%Y A020829 Cf. A131594 (regular octahedron volume), A102208 (regular icosahedron volume), A102769 (regular dodecahedron volume).
%Y A020829 Cf. A010524, A020765, A020775, A378207.
%K A020829 nonn,cons,easy
%O A020829 0,3
%A A020829 _N. J. A. Sloane_