Re: "frac2" button

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Re: "frac2" button

First of all, the TI-92 does symbolic math, but once you approximate
your numbers, you are not much better off than you are on the '85.  The
"exact()" command is not foolproof: do divination there.  Take a look.
The function

approx(sqrt(2)/2)

will return .70710678118655 for an answer.  In that case,

exact(.70710678118655)

would return sqrt(2)/2, wouldn't it?  Not a chance.  All it gives you is
a large fraction:

14142135623731
--------------
20000000000000

Adjusting the tolerance (a second parameter to adjust for roundoff
errors) does not do any better:

exact(.70710678118655,1*10^-13)

 =   2744210
     -------
     3880899

In short, The TI-92 cannot do this "frac2" stuff.  It is a truly amazing
machine, but don't expect too many miracles.  (Sigh) I guess you have to
figure out the numbers yourself (like multiplying by sqrt(2) in this
example to get approximately 1.) or using better judgement about what
you want your calculator to approximate.

Tavis

Chopps wrote:
>
> then how do you explain how the ti-92 does it?  I want some kind of
> symbolic manipulation, that i hear ppl are working on!!!
>
> RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU> wrote in article
> <01ISU8F74CAUCIRDY1@ritvax.isc.rit.edu>...
>
>
> > As soon as you can input a decimal that is _exactly_ equal to half
> > the square root of 3, then you can start thinking about how to create
> > a "frac2" button that will report this.  But that will be a very long
> > time!
> >
> > The best you can possibly do is make a _guess_ or a _bet_ that the
> > decimal value in your hands was really meant to be an approximation
> > of some particular easily-described irrational value.  If you have
> > some 12- or 13-place representation stored in memory W, for example,
> > you might try using Frac on W^2 and decide whether you like what you
> > see.  Another plausible effort might be to divide W by pi (and try
> > Frac again, maybe).  Of course, what you have might just be a
> > representation of 2 minus the square root of 3, or the
> > cube root of 5 plus the cube root of 7, or pi^2, or some weirder
> > number that you will never guess the secret of.  Calculators are
> > wonderful, but they have no supernatural powers of divination (as far
> > as I know, anyway).  :-)}
> >
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