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A195387 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)). 5
1, 1, 4, 6, 8, 0, 9, 7, 5, 9, 1, 5, 8, 1, 9, 1, 6, 3, 0, 9, 5, 3, 7, 7, 6, 0, 0, 6, 5, 1, 9, 6, 8, 1, 6, 0, 7, 5, 5, 6, 7, 6, 8, 2, 9, 7, 3, 5, 9, 7, 5, 1, 3, 7, 2, 7, 2, 9, 8, 2, 4, 8, 5, 3, 3, 1, 7, 8, 9, 4, 6, 4, 4, 3, 9, 9, 1, 8, 6, 0, 9, 3, 6, 7, 6, 2, 0, 5, 1, 5, 2, 1, 5, 4, 4, 9, 5, 5, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
See A195284 for definitions and a general discussion.
LINKS
EXAMPLE
(B)=1.1468097591581916309537760065196816075567682...
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
Sequence in context: A107648 A004786 A263357 * A326426 A272028 A181097
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
STATUS
approved

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Last modified February 20 17:43 EST 2024. Contains 370215 sequences. (Running on oeis4.)