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A296794
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Decimal expansion of the arc length of the Golden Spiral inscribed inside a Golden Rectangle with a unit width.
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1
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4, 1, 0, 7, 0, 3, 8, 0, 4, 9, 4, 4, 0, 1, 0, 2, 3, 8, 1, 2, 8, 3, 1, 2, 9, 9, 5, 1, 5, 8, 0, 8, 7, 2, 8, 1, 4, 3, 8, 1, 5, 8, 8, 9, 9, 2, 4, 5, 5, 3, 1, 9, 2, 0, 6, 5, 4, 3, 6, 2, 1, 7, 3, 4, 4, 0, 4, 5, 1, 8, 0, 7, 1, 4, 0, 7, 4, 6, 8, 4, 8, 4, 9, 3, 1, 3, 0
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OFFSET
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1,1
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LINKS
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FORMULA
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sqrt(1+1/sqrt(5))*sqrt(1+b^2)/b, where b=2*log(phi)/Pi, and phi=(1+sqrt(5))/2.
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EXAMPLE
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4.10703804944010238128...
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MATHEMATICA
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b=2*Log[GoldenRatio]/Pi; RealDigits[Sqrt[1+1/Sqrt[5]]*Sqrt[1 + b^2]/b, 10, 120][[1]]
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PROG
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(PARI) phi = (1+sqrt(5))/2; b = 2*log(phi)/Pi; sqrt(1+1/sqrt(5))*sqrt(1+b^2)/b \\ Michel Marcus, Dec 23 2017
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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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