On 17 Dec 2003, at 23:38, Dwight K. Elvey wrote:
> Hi
> There was a talk at our last svfig ( Silicon Valley Forth Interest
> Group )
> about how to find the interesting integer ratios ( like 355/113 ).
> Although,
> one can simply try all kinds of numbers ( quite quick on todays
> processors ),
> there are algorithms based on number theory that are faster. I wish I
> was
> paying more attention so I could pass on what was done.
> The talk was based on creating speciallized languages to handle these
> interesting problems of LSD's ( Least Common Denominator ). The fellow
> that gave the talk was named LaFarr. Forth is especially adapt at
> creating application oriented languages. I fact that is the way
> one normally programs in Forth, once they know what they are doing.
> Dwight
The mathematics that you're looking for is called 'continued fractions'.
You can find good descriptions at
http://mathworld.wolfram.com/PiContinuedFraction.html and
http://home.att.net/~numericana/answer/fractions.htm
Interestingly enough, continued fractions can also be used to explain
how both western and Chinese musical scales are derived.
http://www.research.att.com/~njas/sequences/DUNNE/TEMPERAMENT.HTML
To bring this somewhat back on topic, the people at MIT who wrote
HAKMEM were interested in continued fractions too, so it looks like
you're in good company! You can see the relevant sections at
http:/www.inwap.com/pdp10/hbaker/hakmem/cf.html
Cheers,
Brian.
--
My other CAR is a CDR.
Received on Wed Dec 17 2003 - 18:46:17 GMT