cp's OEIS Frontend

A195346 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)=(1,3,sqrt(10)).

%I A195346 #7 Feb 11 2025 12:59:43
%S A195346 1,1,8,4,7,1,8,2,9,4,4,9,2,8,0,0,8,0,2,3,8,8,4,0,7,5,5,9,3,7,6,2,3,9,
%T A195346 8,4,3,3,9,7,4,5,0,7,8,2,2,8,4,7,4,0,8,4,4,1,6,4,9,2,4,4,6,1,1,4,1,8,
%U A195346 8,8,0,6,2,5,7,2,8,1,8,3,5,6,5,7,2,7,2,1,3,2,0,5,5,3,0,0,1,7,4,1
%N A195346 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)=(1,3,sqrt(10)).
%C A195346 See A195284 for definitions and a general discussion.
%H A195346 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%e A195346 (C)=1.1847182944928008023884075593762398433974507...
%t A195346 a = 1; b = 3; c = Sqrt[10]; f = 2 a*b/(a + b + c);
%t A195346 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195346 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195346 x3 = f*Sqrt[2]
%t A195346 N[x1, 100]
%t A195346 RealDigits[%]  (* A195344 *)
%t A195346 N[x2, 100]
%t A195346 RealDigits[%] (* A195345 *)
%t A195346 N[x3, 100]
%t A195346 RealDigits[%] (* A195346 *)
%t A195346 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195346 RealDigits[%] (* A195347 *)
%o A195346 (PARI) sqrt(72)/(sqrt(10)+4) \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A195346 Cf. A195284.
%K A195346 nonn,cons
%O A195346 1,3
%A A195346 _Clark Kimberling_, Sep 16 2011