OFFSET
1,2
COMMENTS
EXAMPLE
length of Philo line: 1.6736473041529...
endpoint on x axis: (1.44062, 0); see A197140
endpoint on line y=2x: (0.765782, 1.53156)
MATHEMATICA
f[t_] := (t - k*t/(k + m*t - m*h))^2 + (m*k*t/(k + m*t - m*h))^2;
g[t_] := D[f[t], t]; Factor[g[t]]
p[t_] := h^2 k + k^3 - h^3 m - h k^2 m - 3 h k t + 3 h^2 m t + 2 k t^2 - 3 h m t^2 + m t^3 m = 2; h = 1; k = 1; (* slope m, point (h, k) *)
t = t1 /. FindRoot[p[t1] == 0, {t1, 1, 2}, WorkingPrecision -> 100]
RealDigits[t] (* A197140 *)
{N[t], 0} (* endpoint on x axis *)
{N[k*t/(k + m*t - m*h)],
N[m*k*t/(k + m*t - m*h)]} (* endpt on line y=mx *)
d = N[Sqrt[f[t]], 100]
RealDigits[d] (* A197141 *)
Show[Plot[{k*(x - t)/(h - t), m*x}, {x, 0, 2}],
ContourPlot[(x - h)^2 + (y - k)^2 == .001, {x, 0, 4}, {y, 0, 3}], PlotRange -> {0, 1.7}, AspectRatio -> Automatic]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 11 2011
STATUS
approved