A196823 - OEIS

%I #16 Feb 10 2015 12:26:10

%S 0,9,3,7,9,0,0,2,2,4,4,3,5,8,8,1,4,0,6,4,6,8,9,1,6,2,7,2,0,2,1,0,9,9,

%T 8,6,7,0,9,0,1,2,8,8,0,7,8,5,3,3,2,8,7,2,7,1,6,2,8,5,9,7,3,8,8,1,3,4,

%U 8,9,3,1,0,9,7,8,6,5,5,8,9,5,2,4,9,0,1,4,9,2,3,8,4,3,1,1,5,3,8,4

%N Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=-c+cos(x), and 0<x<2*Pi.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WitchofAgnesi.html">Witch of Agnesi</a>

%e c=0.09379002244358814064689162720210998670901288078533287...

%t Plot[{1/(1 + x^2), -.094 + Cos[x]}, {x, 0, 1}]

%t t = x /. FindRoot[2 x == ((1 + x^2)^2) Sin[x], {x, .5, 1}, WorkingPrecision -> 100]

%t RealDigits[t]     (* A196822 *)

%t c = N[-Cos[t] + 1/(1 + t^2), 100]

%t RealDigits[-c]     (* A196823 *)

%t slope = N[-Sin[t], 100]

%t RealDigits[slope] (* A196824 *)

%Y Cf. A196822.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Oct 06 2011

%E 0 prepended to get correct constant value by _Michel Marcus_, Feb 10 2015