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A101465
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Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.
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6
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5, 8, 5, 7, 8, 6, 4, 3, 7, 6, 2, 6, 9, 0, 4, 9, 5, 1, 1, 9, 8, 3, 1, 1, 2, 7, 5, 7, 9, 0, 3, 0, 1, 9, 2, 1, 4, 3, 0, 3, 2, 8, 1, 2, 4, 6, 2, 3, 0, 5, 1, 9, 2, 6, 8, 2, 3, 3, 2, 0, 2, 6, 2, 0, 0, 9, 2, 6, 7, 5, 2, 1, 5, 3, 7, 8, 9, 2, 9, 6, 1, 1, 4, 9, 6, 1, 2, 4, 6, 5, 6, 7, 2, 3, 5, 8, 4, 2, 7, 2, 6, 4, 9, 8, 6
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OFFSET
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0,1
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COMMENTS
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This also equals the probability, for a random walk on the slit plane starting at (1,0), of stopping at the origin.
This is the least real number m such that m*(sqrt(ab) + sqrt(bc) + sqrt(ca)) + sqrt(a^2+b^2+c^2) >= a+b+c where a,b,c are positive real numbers with ab+bc+ca > 0. See the Mathematical Reflections link.
The asymptotical ratio of odd to even powerful numbers (Srichan, 2020). - Amiram Eldar, Mar 07 2021
The volume of the solid formed by the intersection of 3 right circular unit-diameter cylinders whose axes are mutually orthogonal and intersect at a single point (Moore, 1974). - Amiram Eldar, Nov 22 2021
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LINKS
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Mireille Bousquet-Mélou and Gilles Schaeffer, Walks on the slit plane, Probability Theory and Related Fields, Vol. 124, No. 3 (2002), pp. 305-344; arXiv preprint, arXiv:0012230 [math.CO], 2000.
Eric Weisstein's World of Mathematics, Octagon.
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EXAMPLE
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0.585786437626904951198311275790301921430328124623051926823320262...
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MATHEMATICA
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RealDigits[2 - Sqrt[2], 10, 100][[1]] (* G. C. Greubel, Oct 01 2018 *)
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PROG
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(Magma) SetDefaultRealField(RealField(100)); 2 - Sqrt(2); // G. C. Greubel, Oct 01 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 20 2005
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STATUS
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approved
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