From: Gerry Myerson <gerry@mpce.mq.edu.au>
Subject: Re: continued fraction of (a+SQR(b))/c
Date: Fri, 19 May 2000 15:49:15 +1000
Newsgroups: sci.math
Summary: [missing]

In article <3923D17E.AAAB254C@netscape.com>, Allen JKeirstead 
<mathmusical@netscape.com> wrote:

> I would love to check this reference out. Thank you for the name of the
> book. I live in the country about 800 kilometers from any library that
> would have that book. 

In that case, here's a summary. To expand z = (m_0 + sqrt d)/q_0, 
where q_0 divides d - (m_0)^2, let s be the integer part of sqrt d.  
Then, for i = 1, 2, ..., let [x] mean integer part of x and let 

a_{i - 1} = [ (m_{i - 1} + s)/q_{i - 1} ], 

m_i = a_{i - 1} q_{i - 1} - m_{i - 1}, 

q_i = q_{i - 2} + a_{i - 1} (m_{i - 1} - m_i). Exception to this last 
is that q_1 = (d - (m_1)^2)/q_0. 

Then the a_i are the partial quotients. 

Gerry Myerson (gerry@mpce.mq.edu.au)