A195357 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)=(2,3,sqrt(13)).

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

Offset: 1

Author

Clark Kimberling, Sep 16 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(C)=1.97204829827269041398021951202570840328458843078514...
		

Crossrefs

Cf. A195284.

Programs

Mathematica

a = 2; b = 3; c = Sqrt[13]; f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%](* (A) A195355 *)
N[x2, 100]
RealDigits[%](* (B) A195356 *)
N[x3, 100]
RealDigits[%](* (C) A195357 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%](* Philo(ABC,I) A195358 *)