The Buffon Needle Problem and a Computer Simulation
One can calculate the value of PI by dropping a needle of length k
onto a grid of parallel lines whose length is greater than k.
The value is determined as the probability of hits (the needle crosses
a grid line) to the total number of tosses. This value is
PI = ( 2 * k * totaltosses) / numberofhits
This calculation was simulated with a computer program.
The program was run on several platforms and processors.
I ran the simulation for 10 million tosses and a needle length of .8.
I assumed the grid lines to be one unit apart.
The results are given below.
Results of Buffon Needle Simulation
 Pentium 133mhz  486DX 120mhz
 Sparc Ultra I  486DX 66mhz 
 DOS  Linux  Solaris 2.5  DOS  Solaris 2.5.1
 Linux 
Time (seconds)  57  32
 123  110
 47  145 
Value of PI  3.163097  3.141706
 3.161965  3.163097
 3.161965 
3.141706 
Note the relatively poor values of PI for the DOS and Solaris OSes. Since
the simulation relies on a random number generator  the results reflect
a possible shortcoming (bug ?) in the generators. Hmmmm. Well boys and girls
we'll have to investigate further.
Any Comments?
And for you linux supporters  it appears that linux on 133 pentium
beat out a Sun Sparc Ultra I (at least for this simulation which gets
the cosine of an angle for each toss of the needle).
For your amusement I have a new simulator  java applet to calculate PI
(I lost the original executable file)
Value of PI (to 10k places) is HERE
Next week there will be a test  to see if you have memorized the value.
