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A247553
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Decimal expansion of A(rectangles), an analog of Moser's worm constant, which is associated with the class of rectangular regions of the plane.
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0
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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, 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, 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
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, p. 492.
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LINKS
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FORMULA
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A = beta*sqrt(1 - beta^2), where beta is A240969.
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EXAMPLE
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0.39438476883681362825403921854319968160795399...
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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