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A020829
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Decimal expansion of 1/sqrt(72) = 1/(3*2^(3/2)) = sqrt(2)/12.
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12
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1, 1, 7, 8, 5, 1, 1, 3, 0, 1, 9, 7, 7, 5, 7, 9, 2, 0, 7, 3, 3, 4, 7, 4, 0, 6, 0, 3, 5, 0, 8, 0, 8, 1, 7, 3, 2, 1, 4, 1, 3, 9, 3, 2, 2, 9, 4, 8, 0, 7, 9, 0, 0, 6, 0, 9, 8, 0, 5, 6, 6, 4, 4, 8, 3, 2, 5, 6, 1, 0, 3, 9, 8, 7, 1, 8, 4, 2, 2, 5, 3, 2, 3, 7, 5, 3, 2, 2, 9, 4, 5, 2, 7, 3, 0, 3, 4, 6, 4
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OFFSET
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0,3
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COMMENTS
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In the dragon curve fractal, (5/6)*sqrt(2) = 1.1785.... is the maximum distance of any point from curve start. Such a maximum must be to a vertex of the convex hull. Hull vertices are shown by Benedek and Panzone (theorem 3, page 85) and their P8 = 7/6 - (1/6)i at distance sqrt((7/6)^2 + (1/6)^2) is the maximum. - Kevin Ryde, Nov 22 2019
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LINKS
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FORMULA
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Equals Integral_{x=0..Pi/4} sin(x)^2 * cos(x) dx. - Amiram Eldar, May 31 2021
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EXAMPLE
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0.117851130197757920733474...
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MATHEMATICA
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RealDigits[sqrt(2)/12, 10, 50][[1]] (* G. C. Greubel, Jul 06 2017 *)
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PROG
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CROSSREFS
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Cf. A131594 (regular octahedron volume), A102208 (regular icosahedron volume), A102769 (regular dodecahedron volume).
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KEYWORD
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AUTHOR
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STATUS
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approved
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