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A384476 Decimal expansion of the smallest interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.

%I A384476 #17 May 31 2025 11:05:31
%S A384476 1,8,6,8,1,6,2,4,8,6,5,0,8,3,5,1,7,7,7,5,8,0,3,4,7,3,3,3,8,5,9,1,6,7,
%T A384476 7,0,3,5,1,5,4,5,2,1,9,5,2,8,0,5,8,5,2,1,2,8,3,9,1,5,5,9,1,8,4,5,7,8,
%U A384476 4,8,9,4,1,0,6,2,3,7,6,5,1,0,7,1,7,1,0,8,1,0,2,6,3,3,4,2,0,7,4,7
%N A384476 Decimal expansion of the smallest interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.
%D A384476 Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.
%H A384476 Stefano Spezia, <a href="/A384474/a384474.png">Albrecht Dürer's approximate construction of the regular pentagon</a>.
%H A384476 Stefano Spezia, <a href="/A384476/a384476.png">Exact form of the constant</a>.
%H A384476 Wikipedia, <a href="https://en.wikipedia.org/wiki/Albrecht_Dürer">Albrecht Dürer</a>.
%F A384476 Equals (3*Pi - 2*A384474 - A384478)/2.
%e A384476 1.868162486508351777580347333859167703515452195...
%t A384476 RealDigits[Pi + ArcTan[(-10 + 10 Sqrt[3] + 2 Sqrt[-4 + 6 Sqrt[3]] +2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] -3 Sqrt[2 (8 - 2 Sqrt[3] -Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])])/(2 + 2 Sqrt[3] + 2 Sqrt[6 (-2 + 3 Sqrt[3])] - 4 Sqrt[-4 + 6 Sqrt[3]] - 2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] - 3 Sqrt[2 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] +Sqrt[-4 + 6 Sqrt[3]])])],10,100][[1]]
%Y A384476 Cf. A228719, A384475 (in degrees).
%Y A384476 Cf. A384473, A384474, A384477, A384478.
%K A384476 nonn,cons
%O A384476 1,2
%A A384476 _Stefano Spezia_, May 30 2025