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A195405 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio). 5
9, 2, 4, 8, 7, 5, 3, 9, 1, 0, 5, 0, 2, 2, 5, 1, 3, 0, 6, 6, 2, 6, 2, 5, 1, 7, 3, 5, 1, 2, 7, 4, 5, 4, 1, 0, 7, 5, 2, 6, 0, 3, 3, 5, 1, 6, 5, 1, 0, 7, 9, 4, 9, 3, 7, 5, 4, 9, 9, 2, 8, 7, 4, 8, 9, 5, 6, 7, 6, 4, 5, 9, 7, 1, 1, 9, 6, 7, 4, 8, 8, 3, 6, 5, 6, 5, 2, 1, 1, 4, 4, 1, 6, 1, 0, 2, 5, 4, 6, 0 (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

(C)=0.92487539105022513066262517351274541075260...

MATHEMATICA

a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;

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) A195403 *)

N[x2, 100]

RealDigits[%]    (* (B) A195404 *)

N[x3, 100]

RealDigits[%]    (* (C) A195405 *)

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

RealDigits[%]    (*  Philo(ABC, I) A195406 *)

CROSSREFS

Cf. A195284.

Sequence in context: A176517 A020784 A111188 * A089065 A248319 A154398

Adjacent sequences:  A195402 A195403 A195404 * A195406 A195407 A195408

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified September 20 20:12 EDT 2019. Contains 327247 sequences. (Running on oeis4.)