

A195436


Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the 1,1,sqrt(2) right triangle ABC.


3



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

0,1


COMMENTS

See A195304 for definitions and a general discussion.


LINKS

Table of n, a(n) for n=0..99.


EXAMPLE

Philo(ABC,G)=0.636258821061838308391049464710...


MATHEMATICA

a = 1; b = 1; h = 2 a/3; k = b/3;
f[t_] := (t  a)^2 + ((t  a)^2) ((a*k  b*t)/(a*h  a*t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f1 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (A) A195433 *)
f[t_] := (t  a)^2 + ((t  a)^2) (k/(h  t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f2 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (B)=sqrt(8/9), 1+A179587 *)
f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h  a*t)/(b*t  a*k))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f3 = (f[t])^(1/2) /. Part[s, 1]
RealDigits[%, 10, 100] (* (C) A195433 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC, G) A195436 *)


CROSSREFS

Cf. A195304.
Sequence in context: A248580 A008567 A233700 * A194625 A165065 A069938
Adjacent sequences: A195433 A195434 A195435 * A195437 A195438 A195439


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Sep 18 2011


STATUS

approved



