A195369 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,sqrt(2),sqrt(3)).

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

Offset: 0

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=0.7157901359899149545954926723334324945663...
		

Links

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

Crossrefs

Cf. A195284, A195370, A195371, 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 *)