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 ;
- }