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.