

A195381


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


5



1, 3, 2, 3, 1, 6, 9, 0, 7, 6, 4, 9, 9, 2, 1, 4, 9, 9, 5, 4, 0, 3, 0, 7, 3, 6, 2, 4, 7, 3, 5, 2, 1, 7, 4, 8, 9, 9, 9, 5, 4, 9, 4, 0, 5, 6, 1, 3, 9, 5, 5, 1, 0, 5, 7, 5, 7, 9, 8, 4, 7, 1, 7, 2, 2, 4, 2, 3, 1, 5, 9, 5, 8, 7, 8, 9, 4, 2, 1, 0, 7, 7, 7, 2, 4, 1, 5, 1, 1, 8, 3, 4, 1, 3, 0, 7, 2, 2, 0, 9
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OFFSET

1,2


COMMENTS

See A195284 for definitions and a general discussion.


LINKS

Table of n, a(n) for n=1..100.


FORMULA

Equals sqrt(12)/phi^2, where phi = A001622.  Jon Maiga, Nov 14 2018


EXAMPLE

(A)=1.32316907649921499540307362473521748999...


MATHEMATICA

a = 2; b = Sqrt[5]; c = 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) A195381 *)
N[x2, 100]
RealDigits[%] (* (B) A195383 *)
N[x3, 100]
RealDigits[%] (* (C) A195384 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195385 *)
RealDigits[Sqrt[12] / ((1 + Sqrt[5]) / 2)^2, 10, 100] (* Vincenzo Librandi, Nov 15 2018 *)


PROG

(MAGMA) Sqrt(12) / ((1 + Sqrt(5)) / 2)^2; // Vincenzo Librandi, Nov 15 2018


CROSSREFS

Cf. A195284, A195383, A195384, A195385.
Sequence in context: A165026 A289773 A197475 * A144558 A307551 A220344
Adjacent sequences: A195378 A195379 A195380 * A195382 A195383 A195384


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Sep 17 2011


STATUS

approved



