Happy Pi day everyone!!

[mpark]

(03-15-2019 12:45 AM)Valentin Albillo Wrote:   
Hi, all:
       
This must be one of the least known ways to compute Pi (no circles, trigonometry or integrals in sight). Here's my implementation for the HP-71B, a user-defined function trivially easy to convert to RPN, RPL or whatever:

       1   DEF FNP(N)
       2       T = N
       3       FOR I = N-1 TO 2 STEP -1
       4             T = CEIL(T/I)*I
       5       NEXT I
       6       FNP = N*N/T
       7   END DEF

It would easily fit in just one line but this way its simplicity might be even clearer.
Let's see the function's value for N = 10, 100, ..., 1000000:

DESTROY ALL @ FIX 5

FNP(10)          -> 2.94118
FNP(100)         -> 3.09215
FNP(1000)        -> 3.13903
FNP(10000)       -> 3.14133
FNP(100000)      -> 3.14153
FNP(1000000)     -> 3.14159

The limit for  N -> Inf   is exactly Pi, of course.

Happy  Pi  Day !

V.
 

What the heck!? How does that even work?