A195301 - OEIS

A195301

Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,1,sqrt(2)).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

EXAMPLE

(A)=0.63405067112442885068505288534396221319891000...

MATHEMATICA

a = 1; b = 1; c = Sqrt[2];

h = a (a + c)/(a + b + c); k = a*b/(a + b + c);

f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2;

s = NSolve[D[f[t], t] == 0, t, 150]

f1 = (f[t])^(1/2) /. Part[s, 1]

RealDigits[%, 10, 100] (* (A) A195301 *)

f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2

s = NSolve[D[f[t], t] == 0, t, 150]

f3 = (f[t])^(1/2) /. Part[s, 4]

RealDigits[%, 10, 100] (* (B)=(A) *)

f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2

s = NSolve[D[f[t], t] == 0, t, 150]

f2 = (f[t])^(1/2) /. Part[s, 1]

RealDigits[%, 10, 100] (* (C) A163960 *)

(f1 + f2 + f3)/(a + b + c)

RealDigits[%, 10, 100] (* Philo(ABC, I), A195303 *)

CROSSREFS

Cf. A195284, A195303, A195304.

Sequence in context: A117042 A227989 A189088 * A196824 A309988 A275835

Adjacent sequences: A195298 A195299 A195300 * A195302 A195303 A195304

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 14 2011

STATUS

approved