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Search: id:A103712
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| A103712 |
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Decimal expansion of the expected distance from a randomly selected point in the unit square to its center. |
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+0
4
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| 3, 8, 2, 5, 9, 7, 8, 5, 8, 2, 3, 2, 1, 0, 6, 3, 4, 5, 6, 7, 2, 3, 8, 3, 0, 0, 8, 1, 9, 8, 2, 4, 8, 3, 9, 7, 9, 3, 2, 9, 7, 2, 0, 3, 3, 9, 3, 9, 7, 6, 3, 9, 1, 3, 9, 8, 8, 3, 2, 9, 2, 2, 4, 4, 4, 0, 6, 8, 4, 9, 4, 3, 7, 8, 0, 6, 8, 8, 8, 5, 4, 4, 4, 7, 3, 4, 9, 0, 7, 1, 0, 3, 9, 6, 4, 9, 6, 0, 2, 5, 9, 8, 6, 2, 5
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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Is it a coincidence that this constant is equal to 1/3 of the ratio of the latus rectum arc of any parabola to its latus rectum (Reese, 2004; Finch, 2005)?
exp(d(2)) - exp(d(2))/Pi = .9994179247351742... ~ 1 - 1/1718. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Feb 21 2005
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, section 8.1.
S. Reese, A universal parabolic constant, 2004, preprint.
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LINKS
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S. R. Finch, Mathematical Constants, addenda, 2005, section 8.1
Eric Weisstein's World of Mathematics, Universal Parabolic Constant
Eric Weisstein's World of Mathematics, Square Line Picking
Eric Weisstein et al., Universal Parabolic Constant
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FORMULA
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This is (sqrt(2) + ln(1 + sqrt(2)))/6.
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EXAMPLE
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0.38259785823210634567238300819824839793297203393976391398832922444...
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MATHEMATICA
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RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/2, 10, 111][[1]] (from Robert G. Wilson v Feb 14 2005)
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CROSSREFS
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Equal to (A002193 + A091648)/6 = (A103710)/6 = (A103711)/3.
Sequence in context: A152230 A118357 A010627 this_sequence A132019 A086178 A016669
Adjacent sequences: A103709 A103710 A103711 this_sequence A103713 A103714 A103715
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Sylvester Reese and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Feb 13 2005
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