cp's OEIS Frontend

A197015 Decimal expansion of the shortest distance from x axis through (3,4) to y axis.

%I A197015 #9 Nov 08 2022 13:14:56
%S A197015 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 A197015 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 A197015 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 A197015 Decimal expansion of the shortest distance from x axis through (3,4) to y axis.
%C A197015 See A197008 for a discussion and guide to related sequences.
%e A197015 d=9.865662555435090192548544326689054243084...
%e A197015 x-intercept=(6.6342...,0)
%e A197015 y-intercept=(0,7.3019...)
%p A197015  3*(1+(4/3)^(2/3))^(3/2); evalf(%) ; # _R. J. Mathar_, Nov 08 2022
%t A197015 f[x_] := x^2 + (k*x/(x - h))^2; t = h + (h*k^2)^(1/3);
%t A197015 h = 3; k = 4; d = N[f[t]^(1/2), 100]
%t A197015 RealDigits[d] (* A197015 *)
%t A197015 x = N[t] (* x-intercept *)
%t A197015 y = N[k*t/(t - h)] (* y-intercept *)
%t A197015 Show[Plot[k + k (x - h)/(h - t), {x, 0, t}],
%t A197015 ContourPlot[(x - h)^2 + (y - k)^2 == .01, {x, 0, 4}, {y, 0, 5}], PlotRange -> All, AspectRatio -> Automatic]
%Y A197015 Cf. A197008.
%K A197015 nonn,cons
%O A197015 1,1
%A A197015 _Clark Kimberling_, Oct 10 2011