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A195383 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)=(2,sqrt(5),3). 5

%I

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

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

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

%N 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)=(2,sqrt(5),3).

%C See A195284 for definitions and a general discussion.

%e (B)=1.354044627772845871283344509104287124060458090...

%t a = 2; b = Sqrt[5]; c = 3; f = 2 a*b/(a + b + c);

%t x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]

%t x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]

%t x3 = f*Sqrt[2]

%t N[x1, 100]

%t RealDigits[%] (* (A) A195381 *)

%t N[x2, 100]

%t RealDigits[%] (* (B) A195383 *)

%t N[x3, 100]

%t RealDigits[%] (* (C) A195384 *)

%t N[(x1 + x2 + x3)/(a + b + c), 100]

%t RealDigits[%] (* Philo(ABC,I) A195385 *)

%Y Cf. A195284.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 17 2011

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)