NAME Dpchrist::TriangularNumber - Perl extension for Triangular numbers. SYNOPSIS use Test::More tests => 1; use Dpchrist::TriangularNumber qw( :all ); ### triangular numbers(): print join(", ", map({ triangular_number($_)} 1..10)), "\n"; ### triangular inverses(): print join(", ", map({ triangular_inverse($_)} 1..10)), "\n"; ### is_triangular_number(): print join(", ", map({ is_triangular_number($_)} 1..10)), "\n"; ok(1); Output: 1..1 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 1, 1.56155281280883, 2, 2.37228132326901, 2.70156211871642, 3, 3.27491721763537, 3.53112887414927, 3.77200187265877, 4 1, , 1, , , 1, , , , 1 ok 1 DESCRIPTION This documentation describes module revision $Revision: 1.26 $. This is alpha test level software and may change or disappear at any time. I was using the following function for games: T(n) = 1 + 2 + ... + (n-1) + n = n * (n+1) / 2 For example: T(1) = 1 T(2) = 3 T(3) = 6 T(4) = 10 T(5) = 15 T(6) = 21 etc. These are called Triangular numbers, after Pascal's Triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 Observe the diagonal numbers starting at the third row: 1, 3, 6, 10, 15, 21. The inverse is given by: n = -0.5 +- sqr(0.25 + 2*T) SUBROUTINES is_triangular_number is_triangular_number EXPR Returns true if EXPR is zero, a triangular number, or the negative of a triangular number. otherwise returns false. triangular_inverse triangular_inverse EXPR Returns triangular inverse of EXPR -- e.g. the inverse of triangular_number(). triangular_number triangular_number EXPR Returns the N-th Triangular number given by EXPR -- e.g. 1, 3, 6, 10, etc.. Note that T(0) = 0, and T(-$n) = -T($n). EXPORT None by default. All of the subroutines may be imported by using the ':all' tag: use Dpchrist::TriangularNumber qw( :all ); INSTALLATION Old school: $ perl Makefile.PL $ make $ make test $ make install Minimal: $ cpan Dpchrist::TriangularNumber Complete: $ cpan Bundle::Dpchrist PREREQUISITES See Makefile.PL in the source distribution root directory. SEE ALSO http://mathforum.org/dr.math/faq/faq.pascal.triangle.html http://mathworld.wolfram.com/TriangularNumber.html http://en.wikipedia.org/wiki/Triangular_numbers AUTHOR David Paul Christensen dpchrist@holgerdanske.com COPYRIGHT AND LICENSE Copyright 2010 by David Paul Christensen dpchrist@holgerdanske.com This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; version 2. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.