A195359 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)=(2,5,sqrt(29)).

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

Offset: 1

Author

Clark Kimberling, Sep 16 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=1.64450806032302424900029973143051331487596632913...
		

Crossrefs

Cf. A195284, A195360, A195361, A195362.

Programs

Mathematica

a = 2; b = 5; c = Sqrt[29]; 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) A195359 *)
N[x2, 100]
RealDigits[%]    (* (B) A195360 *)
N[x3, 100]
RealDigits[%]    (* (C) A195361 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC,I) A195362 *)