cp's OEIS Frontend

A384474 Decimal expansion of the middle interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.

%I A384474 #14 May 31 2025 11:05:24
%S A384474 1,8,9,1,3,4,5,5,9,4,4,4,8,5,1,0,4,1,8,6,8,7,1,7,3,4,7,8,9,5,2,7,3,9,
%T A384474 1,9,9,0,2,4,7,7,9,2,2,5,3,0,7,7,4,6,9,6,6,9,2,7,7,4,8,7,7,0,3,7,2,8,
%U A384474 8,7,5,9,6,9,4,5,8,5,4,4,4,3,1,4,7,8,6,3,2,3,2,3,2,2,6,8,1,0,3,1
%N A384474 Decimal expansion of the middle interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.
%D A384474 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.
%D A384474 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 181-182.
%H A384474 Alexander Bogomolny, <a href="http://www.cut-the-knot.org/pythagoras/DurerPentagon.shtml">Approximate Construction of Regular Pentagon by A. Dürer</a>.
%H A384474 Stefano Spezia, <a href="/A384474/a384474.png">Albrecht Dürer's approximate construction of the regular pentagon</a>.
%H A384474 Wikipedia, <a href="https://en.wikipedia.org/wiki/Albrecht_Dürer">Albrecht Dürer</a>.
%F A384474 Equals 3*Pi/4 - arcsin(sqrt(3)*sin(Pi/12)).
%F A384474 Equals Pi + arctan((3 - sqrt(3) + sqrt(6*sqrt(3) - 4))/(3 - sqrt(3) - sqrt(6*sqrt(3) - 4))).
%F A384474 Equals (3*Pi - 2*A384476 - A384478)/2.
%F A384474 A384476 < this constant < A384478.
%e A384474 1.891345594448510418687173478952739199024779225...
%t A384474 RealDigits[3Pi/4-ArcSin[Sqrt[3]Sin[Pi/12]],10,100][[1]] (* or *)
%t A384474 RealDigits[Pi+ArcTan[(3-Sqrt[3]+Sqrt[6Sqrt[3]-4])/(3-Sqrt[3]-Sqrt[6Sqrt[3]-4])],10,100][[1]]
%Y A384474 Cf. A228719, A384473 (in degrees).
%Y A384474 Cf. A002194, A019824, A177870.
%Y A384474 Cf. A384475, A384476, A384477, A384478.
%K A384474 nonn,cons
%O A384474 1,2
%A A384474 _Stefano Spezia_, May 30 2025