A195366 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)=(sqrt(2),sqrt(3),sqrt(5)).
1, 0, 0, 7, 4, 6, 3, 7, 4, 8, 0, 3, 0, 0, 5, 1, 5, 9, 4, 2, 9, 2, 1, 1, 8, 8, 4, 0, 2, 6, 7, 0, 6, 6, 1, 8, 1, 5, 8, 0, 2, 2, 0, 5, 4, 3, 3, 8, 2, 5, 6, 7, 3, 4, 0, 1, 3, 7, 1, 2, 8, 8, 4, 0, 9, 4, 8, 0, 1, 7, 9, 2, 9, 6, 1, 7, 9, 3, 4, 2, 6, 5, 0, 5, 1, 2, 8, 2, 9, 8, 5, 7, 3, 6, 4, 7, 6, 6, 6, 8
Offset: 1
Examples
(B)=1.007463748030051594292118840267066181580...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A195284.
Programs
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Mathematica
a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5]; 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) A195365 *) N[x2, 100] RealDigits[%] (* (B) A195366 *) N[x3, 100] RealDigits[%] (* (C) A195367 *) N[(x1 + x2 + x3)/(a + b + c), 100] RealDigits[%] (* Philo(ABC,I) A195368 *)
Comments