A195341 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)=(1,2,sqrt(5)).

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

Offset: 0

Author

Clark Kimberling, Sep 16 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			0.898055953159170744883890303595053575158424964642...
		

Links

• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A195284.

Programs

Mathematica

a = 1; b = 2; 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) A195340 *)
N[x2, 100]
RealDigits[%] (* (B) A195341 *)
N[x3, 100]
RealDigits[%] (* (C) A195342 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC,I) A195343 *)

PARI

polrootsreal(x^4 - 100*x^2 + 80)[3] \\ Charles R Greathouse IV, Feb 11 2025

Extensions

a(99)-a(100) corrected by Georg Fischer, Jul 18 2021