A195345 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)=(1,3,sqrt(10)).

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

Offset: 1

Author

Clark Kimberling, Sep 16 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(B)=1.0326414912093473614756376556576114854142201858...
		

Links

• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A195284.

Programs

Mathematica

a = 1; b = 3; c = Sqrt[10]; 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[%]  (* A195344 *)
N[x2, 100]
RealDigits[%] (* A195345 *)
N[x3, 100]
RealDigits[%] (* A195346 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* A195347 *)

PARI

(6*sqrt(20 + sqrt(40)))/(14 + 5*sqrt(10)) \\ Charles R Greathouse IV, Feb 11 2025