A195397 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).

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

Offset

1,2

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=1..100.

Example

(C)=1.6117674029515574301961776191386099256...

Mathematica

a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
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) A195395 *)
N[x2, 100]
RealDigits[%]    (* (B) A195396 *)
N[x3, 100]
RealDigits[%]    (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC, I) A195398 *)

Crossrefs

Cf. A195284.

Sequence in context: A138072 A176348 A176264 * A173741 A171147 A171695

Adjacent sequences: A195394 A195395 A195396 * A195398 A195399 A195400

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved