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%I #5 Sep 19 2014 09:40:14
%S 3,9,4,3,8,4,7,6,8,8,3,6,8,1,3,6,2,8,2,5,4,0,3,9,2,1,8,5,4,3,1,9,9,6,
%T 8,1,6,0,7,9,5,3,9,9,0,3,8,9,3,7,5,1,5,2,2,2,8,8,3,7,3,7,9,0,9,4,0,1,
%U 2,9,3,4,2,3,1,5,0,8,8,0,0,2,0,7,9,1,6,1,8,3,7,7,2,8,8,4,8,0,7,6,6,7
%N Decimal expansion of A(rectangles), an analog of Moser's worm constant, which is associated with the class of rectangular regions of the plane.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, p. 492.
%F A = beta*sqrt(1 - beta^2), where beta is A240969.
%e 0.39438476883681362825403921854319968160795399...
%t phi = ArcSin[1/6 + (4/3)*Sin[(1/3)*ArcSin[17/64]]]; psi = ArcTan[(1/2)*Sec[phi]]; beta = (1/2)*(Pi/2 - phi - 2*psi + Tan[phi] + Tan[psi])^(-1); A = beta*Sqrt[1 - beta^2]; RealDigits[A, 10, 102] // First
%Y Cf. A240969 (beta).
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Sep 19 2014
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