A195395 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).
1, 2, 0, 4, 4, 9, 9, 9, 5, 2, 4, 3, 8, 3, 0, 0, 4, 2, 2, 9, 6, 2, 6, 7, 7, 2, 0, 4, 9, 5, 5, 8, 8, 0, 4, 2, 5, 3, 7, 2, 4, 9, 9, 8, 3, 8, 1, 4, 3, 2, 7, 9, 8, 3, 2, 8, 9, 2, 3, 7, 3, 3, 6, 2, 4, 6, 2, 0, 5, 8, 0, 7, 9, 0, 1, 7, 0, 6, 1, 9, 5, 8, 9, 3, 3, 1, 3, 9, 8, 9, 3, 0, 0, 9, 4, 1, 9, 1, 5, 1
Offset: 1
Examples
(A)=1.204499952438300422962677204955880425372499...
Programs
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Mathematica
a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8]; 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) A195395 *) N[x2, 100] RealDigits[%] (* (B) A195396 *) N[x3, 100] RealDigits[%] (* (C) A195397 *) N[(x1 + x2 + x3)/(a + b + c), 100] RealDigits[%] (* Philo(ABC,I) A195398 *)
Comments