cp's OEIS Frontend

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.

A104957 Decimal expansion of the area of the regular 7-gon (heptagon) of circumradius = 1.

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%I A104957 #30 Aug 29 2025 13:49:13
%S A104957 2,7,3,6,4,1,0,1,8,8,6,3,8,1,0,4,3,3,0,4,7,9,5,5,5,8,4,3,3,5,9,2,0,2,
%T A104957 1,2,5,8,1,3,1,7,0,8,1,5,4,8,0,4,0,6,3,5,1,4,3,2,2,2,2,3,5,3,1,5,7,8,
%U A104957 2,1,0,6,0,7,1,8,7,7,7,5,4,5,9,5,3,0,3,8,0,2,4,1,1,8,4,6,8,4,3,7,8,1,2,9,1
%N A104957 Decimal expansion of the area of the regular 7-gon (heptagon) of circumradius = 1.
%C A104957 Equivalently, the area in the complex plane of the smallest convex set containing all order-7 roots of unity.
%C A104957 The second largest root of 4096*x^6 - 87808*x^4 + 537824*x^2 - 823543 = 0. [Corrected by _Sean A. Irvine_, May 24 2025]
%H A104957 Eric Weisstein et al., <a href="https://mathworld.wolfram.com/RootofUnity.html">Root of Unity</a>.
%H A104957 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/deMoivreNumber.html">de Moivre Number</a>.
%H A104957 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%F A104957 Equals 3*sin(2*Pi/7) - sin(12*Pi/7)/2.
%F A104957 Equals 7*cos(3*Pi/14)/2. - _Amiram Eldar_, Feb 25 2023
%F A104957 A root of 4096*x^6 -87808*x^4 +537824*x^2 -823543=0. - _R. J. Mathar_, Aug 29 2025
%e A104957 2.736410188638104330479555843359202125813170815480406351432222353...
%t A104957 RealDigits[Floor[n/2]*Sin[(2*Pi)/n] - Sin[(4*Pi*Floor[n/2])/n]/2 /. n -> 7, 10, 100][[1]]
%t A104957 RealDigits[Root[-823543 + 537824*#1^2 - 87808*#1^4 + 4096*#1^6 &, 5, 0], 10, 100][[1]]
%o A104957 (PARI) 3*sin((2*Pi)/7) - sin((12*Pi)/7)/2 \\ _Michel Marcus_, Feb 25 2023
%Y A104957 Cf. A104954, A104955, A104956.
%K A104957 nonn,cons,changed
%O A104957 1,1
%A A104957 Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 30 2005