A197015 - OEIS

%I #9 Nov 08 2022 13:14:56

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

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

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

%N Decimal expansion of the shortest distance from x axis through (3,4) to y axis.

%C See A197008 for a discussion and guide to related sequences.

%e d=9.865662555435090192548544326689054243084...

%e x-intercept=(6.6342...,0)

%e y-intercept=(0,7.3019...)

%p  3*(1+(4/3)^(2/3))^(3/2); evalf(%) ; # _R. J. Mathar_, Nov 08 2022

%t f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);

%t h = 3; k = 4; d = N[f[t]^(1/2), 100]

%t RealDigits[d] (* A197015 *)

%t x = N[t] (* x-intercept *)

%t y = N[k*t/(t - h)] (* y-intercept *)

%t Show[Plot[k + k (x - h)/(h - t), {x, 0, t}],

%t ContourPlot[(x - h)^2 + (y - k)^2 == .01, {x, 0, 4}, {y, 0, 5}], PlotRange -> All, AspectRatio -> Automatic]

%Y Cf. A197008.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 10 2011