A195371 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)=(1,sqrt(2),sqrt(3)).

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

Offset: 0

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(C)=0.96472381958991695060440464950380668660...
		

Links

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

Crossrefs

Cf. A195284, A195369, A195370, A195372.

Programs

Mathematica

a = 1; b = Sqrt[2]; c = Sqrt[3];
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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195372 *)