A197001 - OEIS

%I #10 Apr 10 2021 02:05:00

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

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

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

%N Decimal expansion of the slope of the line y=mx which meets the curve y=1+cos(x) orthogonally over the interval [0, 2*Pi] (as in A197000).

%C See the Mathematica program for a graph.

%C xo=1.2488014367215508560475125020128381535587614...

%C yo=1.3164595537507515212878992732671186100622603...

%C m=1.05417844265684217515747734305673483746142104...

%C |OP|=1.81454423617045980814297669595599066552030...

%t c = 1;

%t xo = x /.

%t   FindRoot[x == Sin[x] (c + Cos[x]), {x, 1, 1.3}, WorkingPrecision -> 100]

%t RealDigits[xo] (* A197000 *)

%t m = 1/Sin[xo]

%t RealDigits[m]  (* A197001 *)

%t yo = m*xo

%t d = Sqrt[xo^2 + yo^2]

%t Show[Plot[{c + Cos[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi}],  ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 2}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic]

%Y Cf. A196700, A196996, A197002.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Oct 09 2011