A195299 - OEIS

A195299

Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(28,45,53).

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

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OFFSET

2,1

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

Table of n, a(n) for n=2..100.

EXAMPLE

(C)=

MATHEMATICA

a = 28; b = 45; c = 53;

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, 4]

RealDigits[%, 10, 100] (* (A) A195298 *)

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, 1]

RealDigits[%, 10, 100] (* (B) A195299 *)

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, 4]

RealDigits[%, 10, 100] (* (C)=20*sqrt(2) *)

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

RealDigits[%, 10, 100] (* Phil(ABC, I), A195300 *)

CROSSREFS

Cf. A195284.

Sequence in context: A197820 A064862 A123202 * A095297 A269545 A258983

Adjacent sequences: A195296 A195297 A195298 * A195300 A195301 A195302

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 14 2011

STATUS

approved