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 A195407 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)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio). 5
 5, 1, 2, 5, 2, 2, 2, 7, 2, 3, 6, 2, 2, 2, 5, 3, 7, 9, 2, 6, 3, 5, 4, 9, 4, 5, 5, 8, 1, 0, 7, 3, 5, 5, 1, 6, 9, 4, 7, 8, 2, 1, 9, 0, 8, 2, 6, 1, 4, 2, 4, 2, 5, 7, 4, 2, 0, 1, 3, 0, 4, 2, 4, 3, 2, 2, 0, 8, 9, 6, 5, 5, 7, 2, 5, 0, 5, 7, 7, 4, 0, 5, 1, 8, 9, 2, 2, 1, 3, 7, 8, 5, 6, 1, 3, 0, 7, 0, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A195284 for definitions and a general discussion. LINKS Table of n, a(n) for n=0..99. EXAMPLE (A)=0.51252227236222537926354945581073551694... MATHEMATICA a = b - 1; b = (1 + Sqrt[5])/2; c = Sqrt[3]; 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) A195407 *) N[x2, 100] RealDigits[%] (* (B) A195408 *) N[x3, 100] RealDigits[%] (* (C) A195409 *) N[(x1 + x2 + x3)/(a + b + c), 100] RealDigits[%] (* Philo(ABC, I) A195410 *) CROSSREFS Cf. A195284, A195408, A195409, A195410. Sequence in context: A157823 A159703 A059521 * A011509 A361970 A144738 Adjacent sequences: A195404 A195405 A195406 * A195408 A195409 A195410 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 17 2011 STATUS approved

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Last modified June 2 21:32 EDT 2023. Contains 363100 sequences. (Running on oeis4.)