NAME

Math::NumSeq::MathImageSqrtContinued -- continued fraction expansion of a square root

SYNOPSIS

use Math::NumSeq::MathImageSqrtContinued;
my $seq = Math::NumSeq::MathImageSqrtContinued->new (sqrt => 2);
my ($i, $value) = $seq->next;

DESCRIPTION

This is terms in the continued fraction expansion of a square root. It approaches the root by

                   1   
sqrt(s) = a[1] + ----------- 
                 a[2] +   1
                        -----------
                        a[3] +   1
                               ----------
                               a[4] + ...

The first term a[1] is the integer part of the root, leaving a remainder 0 < r < 1 which is expressed as r=1/R with R > 1. Then a[2] is the integer part of that R, and so on recursively.

Values a[2] onwards always repeat in a fixed sequence. For example sqrt(14) is a[1]=3 and then 1,2,1,6 repeating. For some a single value repeats, for example sqrt(2) is a[1]=1 then 2 repeating.

FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for the behaviour common to all path classes.

$seq = Math::NumSeq::MathImageSqrtContinued->new (sqrt => $s)

Create and return a new sequence object giving the Continued expansion terms of sqrt($s).

SEE ALSO

Math::NumSeq, Math::NumSeq::SqrtEngel, Math::NumSeq::SqrtDigits

Math::Pell, Math::ContinuedFraction