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A195386 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)=(sqrt(2),sqrt(5),sqrt(7)). 5
1, 0, 4, 5, 8, 3, 1, 3, 7, 9, 9, 7, 9, 9, 5, 5, 8, 7, 4, 9, 4, 8, 7, 2, 0, 5, 7, 5, 7, 0, 3, 4, 1, 1, 6, 8, 1, 4, 2, 4, 8, 5, 2, 0, 4, 7, 4, 4, 8, 0, 2, 4, 4, 0, 9, 4, 4, 5, 3, 8, 9, 4, 5, 8, 9, 0, 4, 0, 7, 2, 1, 2, 7, 2, 0, 5, 8, 6, 7, 2, 9, 0, 3, 5, 6, 3, 1, 8, 0, 3, 1, 7, 9, 4, 4, 5, 7, 4, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

EXAMPLE

(A)=1.0458313799799558749487205757034116814248520474480...

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, A195887, A195888, A195389.

Sequence in context: A180307 A263208 A010477 * A259468 A143717 A155921

Adjacent sequences:  A195383 A195384 A195385 * A195387 A195388 A195389

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)