A195396 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).

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

Offset: 1

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(B)=1.2693157988625606692872767327389453984514...
		

Crossrefs

Cf. A195284.

Programs

Mathematica

a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
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) A195395 *)
N[x2, 100]
RealDigits[%]    (* (B) A195396 *)
N[x3, 100]
RealDigits[%]    (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195398 *)