cp's OEIS Frontend

A384473 Decimal expansion of the middle interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

%I A384473 #18 May 31 2025 11:05:20
%S A384473 1,0,8,3,6,6,1,2,0,1,6,2,5,6,1,4,6,7,0,0,8,0,4,6,9,3,5,2,7,7,1,6,4,4,
%T A384473 2,9,8,9,6,1,3,3,4,3,1,0,0,3,4,2,3,5,2,3,9,7,3,8,8,0,2,8,4,3,2,0,7,0,
%U A384473 3,4,6,2,9,1,5,7,9,8,0,4,9,4,1,5,2,1,2,4,6,8,8,1,2,1,0,1,3,3,1,8
%N A384473 Decimal expansion of the middle interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.
%D A384473 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 A384473 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 181-182.
%H A384473 Alexander Bogomolny, <a href="http://www.cut-the-knot.org/pythagoras/DurerPentagon.shtml">Approximate Construction of Regular Pentagon by A. Dürer</a>.
%H A384473 Stefano Spezia, <a href="/A384473/a384473.png">Albrecht Dürer's approximate construction of the regular pentagon</a>.
%H A384473 Wikipedia, <a href="https://en.wikipedia.org/wiki/Albrecht_Dürer">Albrecht Dürer</a>.
%F A384473 Equals 135 - 180*arcsin(sqrt(3)*sin(Pi/12))/Pi.
%F A384473 Equals (Pi + arctan((3 - sqrt(3) + sqrt(6*sqrt(3) - 4))/(3 - sqrt(3) - sqrt(6*sqrt(3) - 4))))*180/Pi.
%F A384473 Equals (540 - 2*A384475 - A384477)/2.
%F A384473 A384475 < this constant < A384477.
%e A384473 108.366120162561467008046935277164429896133431...
%t A384473 RealDigits[(3Pi/4-ArcSin[Sqrt[3]Sin[Pi/12]])180/Pi,10,100][[1]] (* or *)
%t A384473 RealDigits[(Pi+ArcTan[(3-Sqrt[3]+Sqrt[6Sqrt[3]-4])/(3-Sqrt[3]-Sqrt[6Sqrt[3]-4])])180/Pi,10,100][[1]]
%Y A384473 Cf. A228719, A384474 (in radians).
%Y A384473 Cf. A002194, A019824, A072097, A177870.
%Y A384473 Cf. A384475, A384476, A384477, A384478.
%K A384473 nonn,cons
%O A384473 3,3
%A A384473 _Stefano Spezia_, May 30 2025