A195370 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,sqrt(2),sqrt(3)).

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

(B)=0.76813743261553676070153452111928795509267198845...

Mathematica

a = 1; b = Sqrt[2]; c = Sqrt[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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC, I) A195372 *)

Crossrefs

Cf. A195284, A195369, A195371, A195372.

Sequence in context: A245771 A202345 A010512 * A277077 A196913 A091343

Adjacent sequences: A195367 A195368 A195369 * A195371 A195372 A195373

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved