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 A086751 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. 4
 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; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Decimal expansion of the number sin(u'), where u' is the number in [0,2 Pi] such that the line normal to the graph of y = sin x at (u', sin u') passes through the point (3 Pi/4,0).  See A332500. - Clark Kimberling, May 05 2020 LINKS FORMULA Define k(n+1) as k(n) - (k(n)*sqrt(1-k(n)^2) + arcsin(k(n)) - Pi/4). The sequence is the decimal expansion of lim_{n -> infinity} k(n). Equals sqrt(2-2*sqrt(1-d^2))/2, where d = A003957 is the Dottie number. - Gleb Koloskov, Jun 16 2021 EXAMPLE 0.403972753299517... MAPLE 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) ; # R. J. Mathar, May 19 2009 MATHEMATICA digits = 105; Sin[FindRoot[Sin[2*a]/2+a == Pi/4, {a, 1/2}, WorkingPrecision -> digits][[1, 2]]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 21 2014 *) PROG (PARI) solve(x=0, 1, x*sqrt(1-x^2) + asin(x) - Pi/4) \\ Michel Marcus, May 05 2020 (PARI) my(d=solve(x=0, 1, cos(x)-x)); sqrt(2-2*sqrt(1-d^2))/2 \\ Gleb Koloskov, Jun 16 2021 CROSSREFS Cf. A003957. Sequence in context: A246686 A048649 A200008 * A048281 A066273 A028650 Adjacent sequences:  A086748 A086749 A086750 * A086752 A086753 A086754 KEYWORD cons,nonn,easy AUTHOR Jonathan R. Anderson (neo__jon(AT)hotmail.com), Jul 30 2003 EXTENSIONS More terms from Jim Nastos, Sep 05 2003 More digits from R. J. Mathar, May 19 2009 STATUS approved

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Last modified May 25 17:48 EDT 2022. Contains 354071 sequences. (Running on oeis4.)