cp's OEIS Frontend

A197000 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=1+cos(x) orthogonally.

%I A197000 #16 Feb 03 2025 21:29:02
%S A197000 1,2,4,8,8,0,1,4,3,6,7,2,1,5,5,0,8,5,6,0,4,7,5,1,2,5,0,2,0,1,2,8,3,8,
%T A197000 1,5,3,5,5,8,7,6,1,4,3,0,3,6,0,8,2,1,6,3,4,1,4,6,0,2,5,0,2,0,4,4,2,0,
%U A197000 8,5,0,0,0,1,4,5,2,7,2,5,5,3,7,0,6,7,4,7,9,9,7,6,6,0,1,4,2,5,9,6
%N A197000 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=1+cos(x) orthogonally.
%C A197000 See the Mathematica program for a graph.
%e A197000 xo=1.2488014367215508560475125020128381535587614... <------ this constant
%e A197000 yo=1.3164595537507515212878992732671186100622603...
%e A197000 m=1.05417844265684217515747734305673483746142104...
%e A197000 |OP|=1.81454423617045980814297669595599066552030...
%t A197000 c = 1;
%t A197000 xo = x /.
%t A197000   FindRoot[x == Sin[x] (c + Cos[x]), {x, 1, 1.3}, WorkingPrecision -> 100]
%t A197000 RealDigits[xo] (* A197000 *)
%t A197000 m = 1/Sin[xo]
%t A197000 RealDigits[m]  (* A197001 *)
%t A197000 yo = m*xo
%t A197000 d = Sqrt[xo^2 + yo^2]
%t A197000 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]
%o A197000 (PARI) solve(x=1,2, sin(x)*(cos(x)+1)-x) \\ _Charles R Greathouse IV_, Feb 03 2025
%Y A197000 Cf. A197001, A196996, A197002.
%K A197000 nonn,cons
%O A197000 1,2
%A A197000 _Clark Kimberling_, Oct 09 2011