Hi. > I have yet to obtain a copy of Norman's book, but I have taken a quick look > at the introductory chapter on the web. It appears that Norman specifies a > plane rotation in terms of two ratios. These ratios are not necessarily > rational numbers, they could be real numbers. So Norman's "rational > trigonometry" is called "rational" because it deals with ratios, not because > it deals with rational numbers. That said, any angle can be approximated > arbitrarily closely by rational numbers.
I looked through the introduction and I think that you are wrong in a subtle way and that the name "rational" is indeed used to mean rational numbers. You are right to say that the ratios are not necessarily rational in theory, but I think what the new approach gives you is that _if_ all the inputs are rational _then_ everything remains rational. In other words, everything you might want to compute as output is a rational function of the input. This is of course not the case with the usual calculations as e.g. sin(1) is not rational at all. And please note that in practice the input data you get is rational because you measure it with limited precision. - lk ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
