How could one miss this? It's PI day today. Here's a slow converging approximation of PI:

[weiqi@gao] $ cat PI.java
public class PI {
  public static void main(String[] args) {
    double sum = 0.0d;
    for (int i = 1; i < 64000; i++) {
      sum += 6.0/(i*i);
    }
    System.out.println(Math.sqrt(sum));
  }
}
[weiqi@gao] $ javac PI.java
[weiqi@gao] $ java PI
3.1415525815597167

Update: Kyle Cordes, in a trackback, expresses the above algorithm in one line of Ruby:

ruby -e "print (1..64000).inject(0.0) { | sum, i | sum + 6.0 / (i*i) } ** 0.5"
3.141577732895

This is indeed shorter than the Java code but not necessarily easier to comprehend. For example, what does ".inject() {| | }" do?

The clearest expression I can think of is in Mathematica:

In[1] :=
    N[Sqrt[Sum[6/n^2, {n, 1, Infinity}]]]
Out[1] =
    3.14159

The equivalent python code is almost as elegent:

python -c "print sum(6.0/(i*i) for i in range(1, 64000))**0.5"
3.14157773266

Slightly longer, but still shorter than the Ruby code is Common Lisp

clisp -x -q '(sqrt (loop for x from 1 to 64000 sum (/ 6.0 (* x x))))'
3.141363

And the shortest of them all, (drum roll...) belongs to Perl (of course)

perl -e '(∑n=1∞6/n2)½'

Just kidding. :)

Responses[2]

Posted by Weiqi Gao on March 15, 2006 12:37:02 AM CST #