Byrd Wrote:
-------------------------------------------------------
> engbren Wrote:
> -------------------------------------------------------
> > Byrd Wrote:
> >
> -------------------------------------------------------
> >
> > >
> > > If they'd had decimals, the number-happy
> > > Babylonians would have pranced down to Cairo
> > and
> > > nicked the concept in a heartbeat!
> >
> > Hi Byrd,
> >
> > This is an unfortunate statement. There would
> be
> > very little practical benefit to the
> Babylonians
> > from adopting a decimal system over the
> > sexagesimal system they developed. The
> sexagesimal
> > system they developed is well known to contain
> > place value, just in powers of 60 rather than
> > powers of 10. The place value system also
> caters
> > for fractions, again in powers of 60 rather
> than
> > 10. The development of this system is widely
> > thought to have eased the processes of
> > multiplication and division relative to the
> > Egyptian system.
> >
> >
>
> Powers of 60 did ease the processes of
> multiplication and division - but decimals and
> zero would have been a significant leap in
> mathematics. The Babylonians still had to
> approximate pi - and I've read that their value
> was not our 3.14159 (etc) - close but not exact.
> Zeroes and decimals would have given a more
> accurate result.

Hi Byrd,

They had a zero for astronomical calculations. Refer to Neugebauer: [www.jstor.org] . Could you explain for me how a different base to the numbering scheme would allow more precise calculations? For example, computers use binary which is base 2. A calculation undertaken in base 2 (binary) is no more or less accurate than base 10 (decimal). There are certain advantages and disadvantages to the base when dealing with fractions. For example 1/3 in decimals results in a repeating sequence 0.333... in fractional notation 3/10 + 3/100 + 3/1000 ... In sexagesimal, it is simply 20/60.

Regards,
Brendan



Edited 1 time(s). Last edit at 12/23/2022 12:22AM by engbren.