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Search: id:A086751
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| A086751 |
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Decimal expansion of the solution to x*Sqrt(1-x^2)+arcsin(x)=pi/4, or the length of the line connecting the origin to the center of the chord of a circle, centered at 0 and of radius 1, that divides the circle such that 1/4 of the area is on one side and 3/4 is on the other side. |
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+0
1
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| 4, 0, 3, 9, 7, 2, 7, 5, 3, 2, 9, 9, 5, 1, 7, 2, 0, 9, 3, 1, 8, 9, 6, 1, 7, 4, 0, 0, 6, 6, 3, 1, 5, 4, 4, 2, 9, 0, 2, 2, 3, 5, 9, 6, 4, 5, 7, 4, 0, 9, 8, 4, 2, 2, 2, 5, 0, 0, 9, 7, 6, 0, 1, 7, 3, 3, 8, 7, 0, 5, 4, 9, 9, 7, 1, 2, 9, 5, 3, 5, 3, 5, 0, 1, 2, 4, 3, 3, 9, 0, 1, 6, 5, 2, 2, 2, 7, 2, 8, 7, 0, 9, 4, 9, 1
(list; cons; graph; listen)
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OFFSET
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0,1
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FORMULA
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Define k(n+1) to be k(n)-(k(n)sqrt(1-k(n)^2)+arcsin(k(n))-pi/4) The sequence is the decimal expansion of limit_{n -> infinity} k(n).
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EXAMPLE
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0.403972753299517...
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MAPLE
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Digits := 240 ; x := 0.4 ; for i from 1 to 8 do f := sin(2.0*x)+2.0*x-Pi/2.0 ; fp := 2*cos(2*x)+2.0 ; x := x-evalf(f/fp) ; printf("%.120f\n", sin(x)) ; od: x := sin(x) ; read("transforms3") ; CONSTTOLIST(x) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2009]
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CROSSREFS
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Sequence in context: A085655 A153615 A048649 this_sequence A048281 A066273 A028650
Adjacent sequences: A086748 A086749 A086750 this_sequence A086752 A086753 A086754
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KEYWORD
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cons,nonn,easy
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AUTHOR
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Jonathan R. Anderson (neo__jon(AT)hotmail.com), Jul 30 2003
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EXTENSIONS
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More terms from Jim Nastos (nastos(AT)gmail.com), Sep 05 2003
More digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2009
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