Re: OT: Need help with numeric bases

On Tuesday 25 February 2003 4:18 pm, Peter Clark wrote:
> On Tuesday 25 February 2003 09:44 am, H. S. Teoh wrote:
> > Just have it return an empty string in an else-clause. I don't know how
> > Python represents an empty string, but I suspect an 'else: return ""'
> > should do the trick. :-)
>
>         Yes, I suspected that something like that would do the trick,
> except that in my befuddled state last night I didn't trust myself not to
> screw something up. :) Part of my brain was concocting all sorts of ways to
> deal with the recursion, while the other part was saying, "No, stupid, it's
> much easier than that!" So I went to bed.
>
> > >         Next up: floating numbers!
> >
> > Hmm, I had a crack at it this morning, but it turns out to be more tricky
> > than I thought. One reason is that under your system, 2 ash can also be
> > written as 1.8 ash, or 1.78 ash, or even 1.777778 ash. So depending on
> > whether you want to force a specific number of octals/ashals, you'll have
> > the script returning 1.778 ash for 2 ash, etc..
>
>         I don't know, but I had imagined the system to work like this:
>         1
>         1.1
>         1.2
>         1.3
>         1.4
>         1.5
>         1.6
>         1.7
>         1.8
>         2
>
> But then I realized that I was inserting a zero, since "1" is really "1.0"
> and "2" is really "2.0."
>         So, when in doubt, I turn to the old standby: what did the ancient
> Greeks do for fractions and/or decimals? As far as I understand it, they
> didn't have zero, but they had to have something to handle geometry.
>
AFAIK, they only used reciprocals as fractions.  They would differ a fraction
from it's corresponding integer by placing a bar or something over it.
Basically, 1.5 would be represented as 1+1/2, 1.1 as 1+1/10, etc. more
complex fractions/decimals(say, 1.35) would be represented as 1+1/4+1/10.
And they denied that irrationals existed, despite the evidence, which even
they had.