login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195494 Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the right triangle ABC having sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio). 5
6, 3, 1, 7, 0, 4, 6, 2, 0, 4, 1, 6, 6, 7, 9, 6, 8, 2, 9, 8, 0, 6, 1, 4, 4, 4, 6, 4, 1, 6, 4, 7, 6, 0, 8, 3, 3, 4, 2, 8, 5, 0, 2, 9, 6, 8, 3, 1, 0, 3, 5, 0, 6, 6, 4, 3, 3, 8, 3, 1, 3, 0, 2, 6, 2, 7, 8, 1, 5, 8, 1, 7, 4, 0, 4, 4, 1, 6, 7, 8, 8, 4, 7, 9, 7, 0, 1, 9, 2, 0, 0, 2, 5, 2, 0, 4, 3, 0, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
See A195304 for definitions and a general discussion.
LINKS
EXAMPLE
Philo(ABC,G)=0.631704620416679682980614446416476083...
MATHEMATICA
a = 1; b = Sqrt[GoldenRatio]; 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) A195491 *)
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) A195492 *)
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, 4]
RealDigits[%, 10, 100] (* (C) A195493 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC, G) A195494 *)
CROSSREFS
Cf. A195304.
Sequence in context: A066717 A176395 A309646 * A154969 A192741 A240264
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 19 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)