cp's OEIS Frontend

A195342 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)=(1,2,sqrt(5)).

%I A195342 #7 Feb 22 2025 20:36:58
%S A195342 1,0,8,0,3,6,3,0,2,6,9,5,0,9,0,5,8,1,4,4,0,6,1,7,2,6,2,8,1,9,6,3,7,5,
%T A195342 7,0,1,9,8,9,4,6,0,4,8,6,8,0,5,6,2,7,3,9,2,6,7,2,5,3,4,3,6,1,1,7,9,6,
%U A195342 0,2,9,9,6,7,4,7,0,8,2,8,9,5,2,0,6,9,1,4,4,9,4,6,0,3,6,2,4,4,2,3
%N A195342 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)=(1,2,sqrt(5)).
%C A195342 See A195284 for definitions and a general discussion.
%H A195342 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%e A195342 (C)=1.0803630269509058144061726281963757019894604...
%t A195342 a = 1; b = 2; c = Sqrt[5]; f = 2 a*b/(a + b + c);
%t A195342 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ];
%t A195342 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ];
%t A195342 x3 = f*Sqrt[2];
%t A195342 N[x1, 100]
%t A195342 RealDigits[%] (* (A) A195340 *)
%t A195342 N[x2, 100]
%t A195342 RealDigits[%] (* (B) A195341 *)
%t A195342 N[x3, 100]
%t A195342 RealDigits[%] (* (C) A195342 *)
%t A195342 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195342 RealDigits[%] (* Philo(ABC,I) A195343 *)
%o A195342 (PARI) 4*sqrt(2)/(3 + sqrt(5)) \\ _Charles R Greathouse IV_, Feb 22 2025
%Y A195342 Cf. A195284.
%K A195342 nonn,cons
%O A195342 1,3
%A A195342 _Clark Kimberling_, Sep 16 2011