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A309282
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Decimal expansion of the circumference of a golden ellipse with a unit semi-major axis.
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1
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5, 1, 5, 4, 2, 7, 3, 1, 7, 8, 0, 2, 5, 8, 7, 9, 9, 6, 2, 4, 9, 2, 8, 3, 5, 5, 3, 9, 1, 1, 3, 3, 4, 1, 9, 5, 5, 2, 8, 7, 9, 7, 2, 2, 3, 5, 7, 0, 8, 6, 6, 1, 8, 2, 0, 7, 2, 9, 7, 2, 0, 0, 0, 2, 0, 5, 3, 9, 4, 3, 8, 1, 1, 3, 6, 1, 1, 0, 4, 6, 2, 2, 8, 4, 7, 8, 5
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OFFSET
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1,1
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COMMENTS
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A golden ellipse is an ellipse inscribed in a golden rectangle. The concept of a golden ellipse was introduced by H. E. Huntley in 1970.
The aesthetic preferences of rectangles and ellipses with relation to the golden ratio were studied by Gustav Fechner in 1876. His results for ellipses were published by Witmer in 1893.
A golden ellipse with a semi-major axis 1 has a minor semi-axis 1/phi and an eccentricity 1/sqrt(phi), where phi is the golden ratio (A001622).
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LINKS
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H. E. Huntley, The Golden Ellipse, The Fibonacci Quarterly, Vol. 12, No. 1 (1974), pp. 38-40.
Eric Weisstein's World of Mathematics, Ellipse.
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FORMULA
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Equals 4*E(1/phi), where E(x) is the complete elliptic integral of the second kind.
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EXAMPLE
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5.154273178025879962492835539113341955287972235708661...
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MATHEMATICA
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RealDigits[4 * EllipticE[1/GoldenRatio], 10, 100][[1]]
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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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