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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.
15
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, 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, 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
OFFSET
1,2
COMMENTS
See the Mathematica program for a graph.
xo=1.2488014367215508560475125020128381535587614...
yo=1.3164595537507515212878992732671186100622603...
m=1.05417844265684217515747734305673483746142104...
|OP|=1.81454423617045980814297669595599066552030...
MATHEMATICA
c = 1;
xo = x /.
FindRoot[x == Sin[x] (c + Cos[x]), {x, 1, 1.3}, WorkingPrecision -> 100]
RealDigits[xo] (* A197000 *)
m = 1/Sin[xo]
RealDigits[m] (* A197001 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
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]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 09 2011
STATUS
approved