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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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3
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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; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| S. R. Finch, Mathematical Constants, Cambridge, 2003, section 8.1.
S. Reese, A universal parabolic constant, 2004, preprint.
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LINKS
| S. R. Finch, Mathematical Constants, addenda, 2005, section 8.1
S. Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, February 2, 2005
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
Wikipedia, Universal parabolic constant
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FORMULA
| This is (sqrt(2) + ln(1 + sqrt(2)))/6.
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EXAMPLE
| 0.38259785823210634567238300819824839793297203393976391398832922444...
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MATHEMATICA
| RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/2, 10, 111][[1]] (from Robert G. Wilson v Feb 14 2005)
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CROSSREFS
| Equal to (A002193 + A091648)/6 = (A103710)/6 = (A103711)/3.
Sequence in context: A195426 A202537 A010627 * A132019 A086178 A016669
Adjacent sequences: A103709 A103710 A103711 * A103713 A103714 A103715
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KEYWORD
| cons,easy,nonn
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AUTHOR
| Sylvester Reese and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Feb 13 2005
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