Re: TI-89: Conics, and Algebra II
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Re: TI-89: Conics, and Algebra II
Speaking about using a TI-89, Donnie Bielak writes:
> Is it possible to do stuff with conics? As in, input the equation and
> have it evaluate whether its a parabola, circle, elipse, or hyperbola
> and have it find the focus, vertices, axis of symmetry, directrix,
> center, radius, major axis, minor axis, slope of asymptotes,
> transverse axis, conjugate axis, ALL THAT GOOD STUFF! Maybe print
> some graphs out too... I want to know what it can do! Any other
> Algebra and Geometry would sure be usefull.... any programs out there
> (or just some info on if they can be made). Any info would be much
> appreciated since Im a newbie. Thanks.
You can do, with a TI-89, just about anything you can do with a pencil
(and a lot more too, of course). There is no question that it takes some
study and experimentation to figure out how to make the calculator (or the
pencil, for that matter) do this or that, but there is a lot of point in the
exploration -- namely, that's how you _learn_ the subject. What this really
means is _internalizing_ the ideas involved, so that you can apply them in a
variety of situations.
There is some question about just how much you want to make the calculator do
automatically, how much you want the calculator to do with assistance from the
user, and how much you want to do yourself just by inspection. The simple
phrase "input the equation" provides an example. Suppose you enter a
second-degree equation in x and y literally, as it sits, from a book or
whatever (the equation itself can be assigned a name such as e1, if you like).
You could develop a general-purpose function on the 89, using its powerful
string-processing capabilities, to search through this equation for an
occurrence of x*x or x^2, strip off the coefficient preceding this, and store
it into a variable such as _a_. You could have the function then search for
each of the other critical coefficients associated with an equation of this
type, and finally return a list {a,b,c,...}.
Most people would not consider this a reasonable expenditure of energy (and
overhead), and prefer to simply enter the equation _as_ a list, using their
eyes and head to determine what the various coefficients are. Or you could
directly enter the various coefficients a, b, c, ... as variables. A simple
calculation involving some of these variables gives you the _characteristic_ of
the equation, a number that tells you whether you have an ellipse, parabola, or
whatever. Again you have a choice -- do you want to enter the formula for the
characteristic directly and just examine the result in order to arrive at your
conclusion, or do you prefer to keep a little program on hand that operates on
the various variables a, b, c, ... (or the _list_ of coefficients if you like),
and then reports back to you (maybe in words) what sort of conic the equation
represents? It's really a question of preferred working style.
Doubtless someone has set up their own set of routines to do the kind of things
the requester wants to do with conics. It is not likely that any second user
would find this particular set of routines an exact match to their needs or
their own preferred working style. And, as they say, "half the fun is getting
there". What would probably be most helpful to new calculator users would
simply be some _clues_ as to how you _might_ do this or that with your
calculator -- opening some doors for exploration. Good examples of ways of
using calculators in mathematical work can often be found in the discussions on
the GRAPH-TI list, in journals such as the Mathematics Teacher, in the
proceedings of the annual ICTCM conferences, etc.
This is all long-term stuff, of course, and none of it is going to help someone
who just wants to do well on a midterm test a week from now -- except to the
extent that trying to get the ideas you have been playing with on paper to also
work on the calculator is going to help you get them into your _head_.
Good luck.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
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