

A195432


Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the 8,15,17 right triangle ABC.


5



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



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)=0.6075103745419345069024584211959403021986468...


MATHEMATICA

a = 8; b = 15; 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) A195429 *)
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) A195430 *)
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) A195431 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC, G) A195432 *)


CROSSREFS

Cf. A195304.
Sequence in context: A021900 A273413 A341906 * A196915 A249651 A021626
Adjacent sequences: A195429 A195430 A195431 * A195433 A195434 A195435


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Sep 18 2011


STATUS

approved



