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The Best Graphing Calculator on the Market?
aaronbeekay asks: "I'm a sophomore in high school taking an honors chem course. I'm being forced to buy something handheld for a calculator (I've been using Qalculate! and GraphMonkey on my Thinkpad until now). I see people all around me with TIs and think 'there could be something so much better'. The low-res, monochrome display just isn't appealing to me for $100-150, and I'd like for it to last through college. Is there something I can use close to the same price range with better screen, more usable, and more powerful? Which high-tech calculators do you guys use?"
It's 12 years old, it's a little slow and they don't make them anymore, but the HP 48 series is a magnificent calculator.
RPN is very nice for long equations. Once you get used to it, you'll be more accurate and efficient. You'll never want to go back to algebraic entry. It has a lot of features, and still stands up pretty well to modern offerings. Unless they've made calculus problems a lot harder, you won't need anything more functionality wise.
The built in equation library is very nice. There is a plethora of available programs to download. The IR sensor is just cool and the keys have the best tactile feel of any calculators ever, and the batteries last about 20 months. Oh, and you could probably dip it in motor oil, and it would still work. The screen while having good contrast, is very fragile however. That's one bad thing.
Expect to pay $250 on ebay for a 48GX unless you get lucky. (The 128K expandable model. Original MSRP was $159 I think) You can probably get a 48G (32KB non expandable model) in your price range though.
RPN is argueably faster, as you don't need to enter in parenthesis. But you end up having to press the enter key a lot, so the advantage quickly evaporates.
A friend of mine at MIT had an HP-48, and I had a TI-81, we used to do a lot of engineering problem sets together and would often race on entering calculations. Averaged over time the competition was a draw. Although the HP-48 definitely wins from a "cool" factor perspective (where cool=geek).
Speaking of the TI-81, I bought mine in 1991 for $82, and I'm still using it every day.
Remember, the generation before yours survived high school and college without the benefit of graphing calculators, and the generation before that used pencil, paper, and tables. Most of them turned out okay.
And you never know when being able to do things by hand is going to save your ass.
I recall a physics exam my freshman year of college, fairly simple mechanics stuff: find how long something takes to slide down a ramp, that sort of thing. About 10 minutes into the hour long exam my calculator blew up. Something in the LCD burst, it was a paperweight.
This was the kind of tech school where the professors just don't give a shit about your issues, and where too many missed exams counted against you heavily; leaving in the middle of one without completing it was the same thing. I was fast enough to get everything but one problem finished with 40 minutes to spare even without the calculator. Only problem was that the answer involved multiplying by the sine of an angle.
I had a couple of sin and cos values memorized: 30 degrees, 60 degrees. Had memorized the square roots of 1 through 5 to a few places, and happened to know how to compute those by hand as well.
Ever come across these formulas?
sin(x/2) = ± sqrt([1 cos x] / 2)
cos(x/2) = ± sqrt([1 + cos x] / 2)
sin(a±b)=sin(a)*cos(b)±sin(b)*cos(a)
Well, if you know sin(30) and cos(30), from these you can compute the values at 15 degrees with a few mathematical operations, then 7.5, then 3.75, etc. Build that little table, and then you can add or subtract things together to reach other values, and maybe throw in a little linear interpolation. Eventually I build an estimate answer using this approach that was close enough to get most of the points for the problem. Got dinged for not using enough significant digits, as if I'd made a rounding error, but got most of the credit.
When time was called I was in the middle of trying to check my answer against the results of a Taylor Series computed with Horner's Rule. Converting degrees to radians by hand is a snap once you've memorized Pi to a thousand places...
Wow... Slashdot fucking /ATE/ my post. Let me try this again...
I recently got a TI-89 Platinum for use in several science (and calculus >_</) courses over the next few years. Despite the fact that the HP-48 and HP-50 are technically superior, and RPN is the fucking win, I chose the TI anyway, and for one reason: software.
There is TONS of homebrewed software out there for TI calcs, and I'm already relatively familiar with m68k assembly, from coding on my C=64 back in the day (though I'm horribly rusty), so I don't have to learn to write for ARMs for the HPs. I also looked for homegrown softs for HP calcs, and found the results wanting.
I have several incredibly useful and easy-to-use chemistry tools, and lots of other good stuff for my TI, and there is a huge community. Not to mention the link software is actually well designed, and easy to use~
Link to huge amounts of TI calc software:
http://www.ticalcs.org/
Shiny. Let's be bad guys.
My friend's father's HP48 was in a briefcase which was left behind during evacuation of the world trade center, somewhere around the 70th floor. 6 months after 9/11, FBI called him up (the evacuated father who made it out) and said "we need you to come down and identify a few items" briefcase made it through with lots of things trashed inside, mostly crushed... but the HP was still working just fine.
strong statement as to their durability.
to email me: take my
That looks cool, but it seems to have too few buttons for my tastes. The main thing I like about my venerable TI-85 is the ease of accessing most of the functions within one, two, or three keypresses. No putzing around with a cursor and joystick. Unless the UI is VERY well designed indeed, I'm skeptical of TI's new system.
If you can prove me wrong, and show that the nspire is as accessible as the TI-85, I might buy one just for day-to-day field engineering needs.
I'm also a Ph.D. student in math (defending my dissertation next month), and I've found the exact opposite to be true. There's no better way to develop a deeper understanding of something than to play with it. As regards calculus and functions, this means plotting functions, composing them, zooming in on them, adding them, differentiating them, multiplying them, etc. This is especially relevant with polar and parametric equations, which can take some time to get the hang of.
The newer calculators even let you play with systems of differential equations and trace out solutions, flow lines, etc. What a great way to learn to visualize otherwise abstract concepts! If students would just sit and play with equations and see what the solutions would look like, they would have a much better grasp of what to expect when they encounter something new. Otherwise, it can tend to be a matter of memorizing a cook book of solution techniques.
Of course, there are times when the calculator can be a hinderance. In particular, the built-in symbolic differentiation and integration can become a crutch. (On the other hand, it's a great way to check your answers.) However, most of the associated problems can easily be dealt with by properly writing your curriculum. (e.g., giving calculator-free exams to test differentiation knowledge, splitting them into two-part exams (without calculator, then with calculator), giving weekly 5-minute self-quizzes, etc.)
At the end of the day, a graphing calculator is just another tool that can be used to help or hinder education. How it goes depends on a combination of student motivation and the leadership and guidance they receive from their professors and teaching assistants. (i.e., you) -- Paul
OpenSource.MathCancer.org: open source comp bio
I'm not sure about your high school but mine required a TI-83+ or TI-84+. Any other was not allowed(most teachers didn't enforce it though). I was also told that I can't use the TI-89 on the SATs although that may have changed. When I got to college I was told I'm not allowed to use a calculator of any sort for anything. When I get to the high level classes I'm allowed to use one but we have Maple which is much more advanced then a normal calculator.
The TI-89 is useful for a whole bunch of other reasons:
* Quick factoring of integers, radicals, polynomials
* Term collection and simplification
* Handling of arbitrarily large values without loss of precision (esp w.r.t. factorials)
* Substitution of variables or expressions in general formulas (user-provided function)
It really can't "solve" very much other than 4th degree polynomial roots. It's really just there to help you manipulate a complex expression without making a mistake (but you really need to be doing the manipulations... which of course requires a bit of knowledge, don't it?)
BTW I distinctly remember adding the incomplete beta and gamma functions to my TI-89, and I think error function too. They would simplify to trivial expressions if they could (to promote further manipulation) or returned numerical solutions if so coerced. I thought it was pretty slick...
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
Then your friend was slow -- or you were very quick. Take some complex expressions and write out the keystrokes required in RPN and infix notations, and you'll see that RPN almost always wins. However, the big win isn't the keystrokes, it's the mental complexity. With infix, you have to maintain too much state in your head -- with particularly nasty expressions, you basically have to keep track of the whole expression in order to enter it all correctly, closing the parentheses at the right times. With RPN, you think about it differently, "collapsing" subexpressions as early as possible, minimizing the amount of you have to hold.
My friends and I ran a series of tests in college, specifically to determine which was more efficient. Not only did the postfix evaluations typically have 10-20% fewer keystrokes, the person writing the postfix version typically finished writing the evaluation while the person writing the infix was still figuring out how to express it. What finally convinced the doubters in our little experiment to buy HPs was that the infix evaluation got the wrong answer much more often than the postfix evaluation did -- usually because of some miscounted parentheses.
RPN is faster, easier and more accurate on complex expressions.
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