Pythagorean Triples

A Stream script to generate pythagorian triples.

#!/usr/bin/perl

use Data::Dumper;
use Stream;

sub nplusone {

  my ($m,$n) = @{$_[0]}; 
  $n == $m+1 ? [1,$n+1] : [$m+1,$n];
}

sub ptrip {

  my ($m,$n) = @{$_[0]}; 
  
  [ ($n**2-$m**2), (2*$n*$m) , ($n**2+$m**2) ];
}

@triples =  sort { $a->[0] <=> $b->[0] || $a->[1] <=> $b->[1] } 
  map { [ sort {$a <=> $b} @$_ ] } 
  iterate(\&nplusone,[1,2])->transform(\&ptrip)->take(1000);

print Dumper(\@triples);
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Re: Pythagorean Triples by Zaxo (Archbishop) on Dec 05, 2002 at 13:54 UTC
Well, somebody's got to do the mathmonk thing. This has a neat relation to number theory. Prime numbers which satisfy `(1 == $prime % 4)` can be expressed as a sum of squares, `($m2 + $n2)`. Such primes can be factored as complex numbers, `$n+i$m` and `$n-i$m` with `$n > $m`. These are known as Gaussian primes. Plugging `$m` and `$n` into your formula shows the correspondence of primes equal to `4*$foo + 1` and Pythagorean right triangles. The ever-popular 3-4-5 right triangle corresponds to the Gaussian prime (2 + i). Not every Pythagorean right triangle corresponds to a Gaussian prime. If $n and $m have a common factor, or are both odd, then they do not represent a complex prime in this way. After Compline, Zaxo	[reply]
(OT) Re: Pythagorean Triples by japhy (Canon) on Dec 05, 2002 at 14:42 UTC
My fraternity's mentor is Pythagoras, and our chief symbol is the right-angled triangle whose sides are proportional to 3, 4, and 5. Just thought I'd chime in with that. `:)` _____________________________________________________ Jeff`[japhy]`Pinyan: Perl, regex, and perl hacker, who'd like a job (NYC-area) `s++=END;++y(;-P)}y js++=;shajsj<++y(p-q)}?print:??;`	[reply]