cp's OEIS Frontend

A195357 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)=(2,3,sqrt(13)).

%I A195357 #5 Mar 30 2012 18:57:45
%S A195357 1,9,7,2,0,4,8,2,9,8,2,7,2,6,9,0,4,1,3,9,8,0,2,1,9,5,1,2,0,2,5,7,0,8,
%T A195357 4,0,3,2,8,4,5,8,8,4,3,0,7,8,5,1,4,3,9,5,8,2,9,8,4,2,7,8,8,5,5,2,7,7,
%U A195357 2,8,7,6,0,2,4,8,3,1,0,9,9,8,6,6,3,5,8,8,8,2,0,5,4,4,2,7,5,8,5,5
%N A195357 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)=(2,3,sqrt(13)).
%C A195357 See A195284 for definitions and a general discussion.
%e A195357 (C)=1.97204829827269041398021951202570840328458843078514...
%t A195357 a = 2; b = 3; c = Sqrt[13]; f = 2 a*b/(a + b + c);
%t A195357 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195357 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195357 x3 = f*Sqrt[2]
%t A195357 N[x1, 100]
%t A195357 RealDigits[%](* (A) A195355 *)
%t A195357 N[x2, 100]
%t A195357 RealDigits[%](* (B) A195356 *)
%t A195357 N[x3, 100]
%t A195357 RealDigits[%](* (C) A195357 *)
%t A195357 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195357 RealDigits[%](* Philo(ABC,I) A195358 *)
%Y A195357 Cf. A195284.
%K A195357 nonn,cons
%O A195357 1,2
%A A195357 _Clark Kimberling_, Sep 16 2011