A195384 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)=(2,sqrt(5),3).

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

Offset

1,2

Comments

See A195284 for definitions and a general discussion.

Links

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

Example

(C)=1.74806409779528428319720482022302045514988...

Mathematica

a = 2; b = Sqrt[5]; c = 3; 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) A195381 *)
N[x2, 100]
RealDigits[%]   (* (B) A195383 *)
N[x3, 100]
RealDigits[%]   (* (C) A195384 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]   (* Philo(ABC, I) A195385 *)

Crossrefs

Cf. A195284.

Sequence in context: A085541 A133055 A303133 * A021576 A222183 A010509

Adjacent sequences: A195381 A195382 A195383 * A195385 A195386 A195387

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved