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From: akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn)
Newsgroups: comp.sys.handhelds
Subject: Re: HP 48 Improved ->Q
Keywords: hp 48 ->q fractions faster better
Message-ID: <27f197fe:2491.2comp.sys.handhelds;1@hpcvbbs.UUCP>
Date: 28 Mar 91 07:40:05 GMT
References: <27e87852:2491comp.sys.handhelds@hpcvbbs.UUCP> <27ed7ff4:2491.1comp
Lines: 62

re: DEC2FRAC by Joseph K. Horn, posted 21 March 1991.

In a followup message, I said:

> ... a completely new algorithm in number theory.  It made my day
> to know that the very first computer to run it was an HP 48SX.

Well, darn it, this is only half true.  It may well be that the 48
has the honors, but the algorithm IS NOT NEW.

Bummer.  I thought I'd discovered something new.  Turns out that I
was 102 years late!!  In a book called _Textbook of Algebra_ by G.
Chrystal, 1st edition in 1889, in Part II, Chapter 32, this improved
continued fraction algorithm is presented and proven.  Odd to tell,
Chrystal speaks of it as if it were ancient knowledge.  The original
discoverer is not named, nor is the algorithm.  Hmmm.  Thanks to
Harry Bertucelli for exhuming this obscure reference.

In any case, it seems to have lay dormant for many years; it is not
mentioned in modern books about number theory.  It's time for us to
revitalize it!  An HP 48 Fraction Library could easily give us the
same power over "fractional objects" that the UNITS menu gives over
unit objects, plus the power of the HP 32SII's ability to handle
fractions as single "objects".

How would you like to be able to divide '2_hr+34_min+56.78_sec' by 4
and see '38_min+44.195_sec'?  Sure, you can use the HMS-> and ->HMS
functions... but why should PEOPLE do what a CALCULATOR should do for
them???  An HP 48 Fraction Library should have:

User-defined unit names and divisors.  Lots of modes: show decimal
after last unit; drop last unit remainder; round last unit; show last
unit as a fraction; maximum allowable denominator; maximum allowable
numerator; maximum allowable numerator AND denominator; force denomi-
nator to always be n; force denominator to always be a factor of n;
allow denominator to be whatever it takes to get the most accuracy;
easy entry of decimal and fractional units...

A few obvious applications are:

yards, feet, inches (e.g. with denominator set to 16ths)
days, hours, min, sec (100ths)
inches, picas, points, HP PCL units (4ths)
gallons, quarts, pints, cups
pounds, shillings, pence, farthings (???)

Everybody has their own messy fractions to deal with every day.
The new thing this library will do is let you specify what YOU want.
It'd make the old "postage stamp problem" trivial to solve.

I just did a bulk rate mailing; 25 raffle tickets per book, two books
per envelope, 10 envelopes per bundle, 20 bundles per sack.  Juggling
uneven sacks isn't difficult math... but I hate it!  It's work that
a machine should do, not a human mind, which should be concerned with
things machines can't do, like what the accompanying letter should
say!  With a Fraction Library it'd be almost pleasant.

If you have any ideas you'd like to see included in a Fraction Library
like this, please post it soon, so that this doesn't become another
dribbleware item.  It'll be freeware, of course.  Right now it's 100%
vaporware, and will be available Real Soon Now.

--  Joseph K. Horn  --  Peripheral Vision, Ltd.  --