Coding for Pi Day

Today is Pi Day, which is a good day to talk about Pi.

Normally, I'd probably use Pi, sine and cosine to draw things, but instead, I flashed on a couple ways to estimate Pi.

Also, showing you can use Unicode characters in Perl.

#!/usr/bin/env perl

use feature qw{ say } ;
use strict ;
use warnings ;
use utf8 ;

my $π = 3.14159 ;

my $est2  = estimate_2() ;
my $diff2 = sprintf '%.5f',abs $π - $est2 ;
say qq{Estimate 2: $est2 - off by $diff2} ;

my $est1  = estimate_1() ;
my $diff1 = sprintf '%.5f',abs $π - $est1 ;
say qq{Estimate 1: $est1 - off by $diff1} ;

exit ;

# concept here is that the area of a circle = π * rsquared
# if r == 1, area = π. If we just take the part of the circle
# where x and y are positive, that'll be π/4. So, take a random
# point between 0,0 and 1,1 see if the distance between it and 
# 0,0 is < 1. If so, we increment, and the count / the number
# so far is an estimate of π.

# because randomness, this will change each time you run it

sub estimate_1 {
    srand ;
    my $inside = 0.0 ;
    my $pi ;
    for my $i ( 1 .. 1_000_000 ) {
        my $x = rand ;
        my $y = rand ;
        $inside++ if $x * $x + $y * $y < 1.0 ;
        $pi = sprintf '%.5f', 4 * $inside / $i ;
        }
    return $pi ;
    }

# concept here is that π can be estimated by 4 ( 1 - 1/3 + 1/5 - 1/7 ...)
# so we get closer the further we go
sub estimate_2 {
    my $pi = 0;
    my $c  = 0;
    for my $i ( 0 .. 1_000_000 ) {
        my $j = 2 * $i + 1 ;
        if ( $i % 2 == 1 ) { $c -= 1 / $j ; }
        else               { $c += 1 / $j ; }
        $pi = sprintf '%.5f', 4 * $c ;
        }
    return $pi ;
    }