A195383 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)=(2,sqrt(5),3).

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

Offset: 1

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(B)=1.354044627772845871283344509104287124060458090...
		

Crossrefs

Cf. A195284.

Programs

Mathematica

a = 2; b = Sqrt[5]; c = 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) A195381 *)
N[x2, 100]
RealDigits[%]   (* (B) A195383 *)
N[x3, 100]
RealDigits[%]   (* (C) A195384 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]   (* Philo(ABC,I) A195385 *)