A195365 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)=(sqrt(2),sqrt(3),sqrt(5)).

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

Offset: 0

Author

Clark Kimberling, Sep 16 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=0.96627396157671295720938864900921248163444...
		

Links

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

Crossrefs

Cf. A195284, A195366, A195367, A195368.

Programs

Mathematica

a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
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) A195365 *)
N[x2, 100]
RealDigits[%]    (* (B) A195366 *)
N[x3, 100]
RealDigits[%]    (* (C) A195367 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]     (* Philo(ABC,I) A195368 *)