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A384475 Decimal expansion of the smallest interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

%I A384475 #17 May 31 2025 11:05:27
%S A384475 1,0,7,0,3,7,8,2,5,9,2,1,5,9,4,1,4,9,4,5,5,1,7,5,9,8,6,0,6,4,5,3,6,1,
%T A384475 6,9,7,7,9,3,9,4,1,8,3,9,4,0,1,5,2,6,8,2,4,8,8,3,8,3,9,7,4,6,7,2,5,2,
%U A384475 5,8,0,7,7,5,1,9,7,9,6,6,7,3,4,8,8,9,3,8,6,7,6,2,6,2,6,6,9,3,5,3
%N A384475 Decimal expansion of the smallest interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.
%D A384475 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 A384475 Stefano Spezia, <a href="/A384473/a384473.png">Albrecht Dürer's approximate construction of the regular pentagon</a>.
%H A384475 Stefano Spezia, <a href="/A384475/a384475.png">Exact form of the constant</a>.
%H A384475 Wikipedia, <a href="https://en.wikipedia.org/wiki/Albrecht_Dürer">Albrecht Dürer</a>.
%F A384475 Equals (540 - 2*A384473 - A384477)/2.
%e A384475 107.03782592159414945517598606453616977939418394...
%t A384475 RealDigits[180(1 + 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]])])]/Pi),10,100][[1]]
%Y A384475 Cf. A228719, A384476 (in radians).
%Y A384475 Cf. A384474, A384476, A384477, A384478.
%K A384475 nonn,cons
%O A384475 3,3
%A A384475 _Stefano Spezia_, May 30 2025