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A195388 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)=(sqrt(2),sqrt(5),sqrt(7)). 5
1, 4, 2, 0, 6, 2, 0, 2, 7, 3, 3, 9, 4, 4, 3, 7, 9, 4, 6, 4, 1, 5, 1, 4, 4, 8, 1, 2, 1, 1, 6, 1, 6, 9, 2, 3, 1, 9, 6, 3, 5, 3, 5, 3, 3, 1, 5, 4, 6, 4, 8, 9, 8, 8, 0, 5, 5, 3, 7, 5, 9, 3, 8, 5, 4, 7, 2, 5, 5, 9, 2, 8, 2, 3, 3, 2, 2, 9, 9, 1, 9, 3, 3, 6, 7, 4, 3, 8, 2, 1, 3, 1, 8, 4, 9, 2, 0, 7, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

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

EXAMPLE

(C)=1.420620273394437946415144812116169231963535...

MATHEMATICA

a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];

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) A195386 *)

N[x2, 100]

RealDigits[%]   (* (A) A195387 *)

N[x3, 100]

RealDigits[%]   (* (A) A195388 *)

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

RealDigits[%]   (* Philo(ABC, I) A195389 *)

CROSSREFS

Cf. A195284.

Sequence in context: A135730 A188595 A144102 * A197813 A200496 A058546

Adjacent sequences:  A195385 A195386 A195387 * A195389 A195390 A195391

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified May 19 04:51 EDT 2013. Contains 225428 sequences.