cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A197136 Decimal expansion of the x-intercept of the shortest segment from the x axis through (4,1) to the line y=x.

Original entry on oeis.org

4, 5, 5, 4, 0, 1, 9, 1, 3, 1, 2, 1, 4, 9, 0, 1, 8, 8, 6, 2, 7, 7, 3, 7, 4, 4, 3, 2, 4, 0, 1, 8, 1, 2, 5, 1, 0, 4, 1, 4, 1, 8, 8, 0, 2, 7, 0, 2, 7, 8, 0, 0, 6, 8, 4, 8, 2, 9, 8, 3, 7, 6, 5, 8, 3, 5, 7, 6, 7, 1, 1, 6, 7, 0, 4, 9, 2, 9, 6, 4, 8, 5, 6
Offset: 1

Views

Author

Clark Kimberling, Oct 10 2011

Keywords

Comments

The shortest segment from one side of an angle T through a point P inside T is called the Philo line of P in T. For discussions and guides to related sequences, see A197008 and A195284.

Examples

			length of Philo line:   3.350162315943772... (see A197137)
endpoint on x axis:   (4.55402, 0)
endpoint on line y=x: (2.93048, 2.93048)
		

Crossrefs

Programs

  • 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 = 1; h = 4; k = 1;(* slope m; point (h,k) *)
    t = t1 /. FindRoot[p[t1] == 0, {t1, 1, 2}, WorkingPrecision -> 100]
    RealDigits[t]  (* A197136 *)
    {N[t], 0} (* endpoint on x axis *)
    {N[k*t/(k + m*t - m*h)],
    N[m*k*t/(k + m*t - m*h)]} (* endpoint on line y=mx *)
    d = N[Sqrt[f[t]], 100]
    RealDigits[d]  (* A197137 *)
    Show[Plot[{k*(x - t)/(h - t), m*x}, {x, 0, 5}],
    ContourPlot[(x - h)^2 + (y - k)^2 == .003, {x, 0, 5}, {y, 0, 3}],
    PlotRange -> {0, 3}, AspectRatio -> Automatic]

Extensions

Incorrect trailing digits removed. - R. J. Mathar, Nov 08 2022