A195399 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(7),3,4).

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

Offset: 1

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=1.75938215709649255886516352490038207092333...
		

Links

• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A195284, A195400, A195401, A195402.

Programs

Mathematica

a = Sqrt[7]; b = 3; c = 4;
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) A195399 *)
N[x2, 100]
RealDigits[%]    (* (B) A195400 *)
N[x3, 100]
RealDigits[%]    (* (C) A195401 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195402 *)

PARI

sqrt(8)*(7-sqrt(7))/7 \\ Charles R Greathouse IV, Nov 26 2024

PARI

polrootsreal(49*x^4-896*x^2+2304)[3] \\ Charles R Greathouse IV, Nov 26 2024