EOS, AOS, RPN/L and more algebra



#9

This whole -3^2 thing has brought out a lot of calculator issues that the prof (and apparently the geometry and beginning algebra profs) isn't addressing. (note: It's not that calculators are required for maths, but they are prevalent, recommended, and "supported" in textbooks.)

I'm not the *only* over 30 in the class, but I am the only one who is being made to retake the class due to length of time out of school instead of coming directly from beginning algebra. I've also got a decade and a half in computer fields and some hobbysit handheld/calc hacking in my book. All of which is simply to say that I got a lot of questions today and have been pushed into the role of calc dude.

Today- I brought my 70's era ti-30 (red led), a friend's modern ti30 variant, an hp48s, 28s, 19bii, and my recently acquired hp20s. Also in class were several other ti30 variants, a ti82 and a ti83+s.

I did go buy a casio fx-115ms because of this (any excuse to blow $15 on a calculator, eh?).

Most people in the class, after spending half of it arguing about precedence, how to simplify equations for calculator input, the usefulness of parens- well, most people seemed to get it. Many of the members of the class are pissed at TI, though. Turns out the casio is an *extremely* approachable calculator with a good equation entering system and a decent solver. Not much memory space, but that's to be expected. It seems to be much more useful than anything else available for that price.

The hp20s gets similarly high marks, but it *might* be out of production and is hard to find anyway.

The RPN calcs were a bit of a difficult concept to explain, but once I got the stack explained adequately, the problem calculation of the day (what people were having trouble with) suddenly became very fun to solve and play with.

(3800ft / pi * 1.3miles)

(with the ti30 calcs, you seem to have to sto the result of

pi * 1.3 * 5280 (converting to feet)

and then recall after entering

3800 / (except that on half the ti's you can't recall in any sane method anyone in class could figure)

RPN I won't even mention, it's a waste of space considering the audience here :)

The casio was: 3800 / (pi * (1.3 * 5280) ) <enter>
Which is remarkably easy. (I added the extrea parens to illustrate the technique if you had other or more complex conversion operations in a similar EQ- such as C to F)

Makes me wonder why TI has such dominance in the market, when dollar for dollar, the casio is much better on the lower end, and the hp has so much more potential if carly will get a sanity pill.
And considering just how basic the casio really is, I'm shocked even more that HP hasn't got a good calc with similar functionality updated, modernized, and available for <$30

-Christof


#10

And considering just how basic the casio really is, I'm shocked even more that HP hasn't got a good calc with similar functionality updated, modernized, and available for <$30

At the risk of blaspheming, I'd guess it has something to do with the fact that both TI and Casio are consumer product businesses and that HP isn't and really has no desire to be there with them, except at the high end (read: high-margin end) of the market. That, and the seemingly pathological loyalty shown by HP's calculator development group (well, when it existed) to the Saturn processor. It is obviously possible -- as demonstrated by TI -- to produce low-cost, feature-rich devices based on a general purpose chip such as a Z80 or 68K. Of course, that would mean HP would have had to start over from scratch. But hey, ya' gotta crack some eggs, right? :^)

#11

Christof wrote: "(with the ti30 calcs, you seem to have to sto the result of

pi * 1.3 * 5280 (converting to feet)

and then recall after entering

3800 / (except that on half the ti's you can't recall in any sane method anyone in class could figure)"

how about:

pi * 1.3 * 5280 = 1/x * 3800 =

Even the first TI calculator would do 1/x (/ = =) using the "CONSTANT memory" (different from "constant MEMORY") although I got a better result in this case with:

3800 / = = * pi * 1.3 * 5280 = / = =

(0.1762787 vs. 0.17594) (8 digit calculator without more internal digits) (with a slide rule you can read "0.176" and guess "0.1762")

or

3800 / pi / 1.3 / 5280 =

(0.1762204)

I apologize if I'm missing the general point. This caught my attention because I've been remembering "dimensional analysis" which I learned in high school chemistry class (pre-calculator). I think it is a natural fit for RPN. Basically, it is a method for doing chain calculations and managing units as you go. Here's what you would do in this example:

(3800 ft/1) * (1/pi) * (1/1.3 mi)

This would have units of "feet/miles", a ratio of two distances, which is a number without units. To eliminate the units, multiply by something equal to 1 in the appropriate units:

(3800 ft/1) * (1/pi) * (1/1.3 mi) * (1 mi/5280 ft)

The first term has feet on the top and the fourth term has feet on the bottom, so those units cancel. Likewise miles in the fourth and third terms. So you eliminate them:

(3800/1) * (1/pi) * (1/1.3) * (1/5280)

Now the result has the desired units - a unit-less ratio of two distances - and the numbers are all laid out to solve with a slide rule - or a calculator. In RPN, it's obvious:

3800 <enter> pi / 1.3 / 5280 /

but not that different with an algebraic calculator:

3800 / pi (=) / 1.3 (=) / 5280 =

(= needed on some calculators)

#12

Hi Christof,

If you get a chance, try the example calculation on a TI-82 vs. a TI-83 -- I'm sure somebody in the class is likely to have these models. The TI-83 has slightly different rules vs. the TI-82, concerning implicit multiplication. The
TI-82 seems to treat implicit multiplication at a higher precedence level vs. multiplication with an explicit multiplication symbol "*".

Note that TI's model 30Xa and 36X have truly awful versions of the ln function which, of course, feed into the y^x function. Taking ln(1 + 1 * 10^-9) yields ONLY 4 accurate decimal places on these models. TI latest scientific calculators, the TI-30XII and TI-34II don't have this problem. The CASIOs, which use a comparable chip to the HP-6S in terms of accuracy are accurate to about 8 decimal places for this ln calculation, if I recall. The HP-20S, on the other hand, returns full accuracy. As does the HP-30S. In fact the accuracy of the HP-30S is incredible.

Among the EOS scientific calculators, the HP-30S is my favorite. But you have to get the latest model -- the earlier model had some bugs -- needless to say this means don't buy this model at Fry's.

Needless to say, there are numerous calculations where the superiority of the HPs shows such as
sin(1 * 10^8 radians). I just wish the 20S had a fraction capability like the 32SII. I also wish that CASIO hadn't made the STO a shifted key on the MS line. However, I do like the concept of making ANS a non-shifted key. Beware also on the CASIOs of the recompute of the previous expression with the STO key. CASIO users [for the MS versions] should get use to the sequence [ANS][STO] ...


#13

About the HP30S, besides the incredible accuracy, I think is directly comparable to the Casio FX 115 MS althoug I prefer the 30S keyboard.

#14

Firstly- some versions of the TI30 have a really hosed approach to 1/x and memories. I mean, REALLY hosed.

Secondly- theln problem is amusing to a few of the students, the prof says "huh. never trust a calculator". Ignorance is bliss and all.....

I haven't used a 30s at all, in fact I haven't seen one. I might have to track one down now. I'm carrying to class my "work" 48sx, a 19bii, 20s, and the casio each day now with different people borrowing and asking as class goes. Kind of fun. I may have to add another bit of weight, then.

I've got pages of notes for a casio manual since that's got the most questions. People either seem to "get" RPN or not, and the 20s is fun,but I'm being cautious letting any pioneer leave my direct physical control nowadays.

-Christof


#15

Hi Christof,

Suggestion --

refer prof and students to the Museum and [among other things] they could play with the various simulations. I think the HP-35 java simulator is awesome including the original HP bugs. The HP-45 simulator is also interesting.
If you have an internet hookup in the classroom, the instructor could bring them up on the screen.

There are zillions [i guess you need a calculator with a three digit exponent to handle zillions :) ] of calculators, some highly specialized to a particular field [frequently a financial field] on the web. There are numerous basic algebraic scientific calculators and of course there is the ****** windows calculator.


#16

no luck on in the classroom- at least not this extension campus.

I have enough calculators to display most major differences (I've got 1970's era 4 bangers and sharp pocket pc type calcs, too. Oh- I even have a ti89 I never use) - I find it interesting that the prof isn't more interested in knowin
g what goes on with them. She seems to get frustrated just with her ti30x on occasion.

I'm having fun encouraging people to buy non TI calcs and showing them *why* I think TI isn't worth gettting below the 83+ level. I nabbed a hp30s this morning to play with- that or the casio wouldbe much more highly recommended than the ti30. I still like the 20s, but it doesn't have that easy to read 2 line system. Well- I prefer to use a 42S or 32SII for that level, but they are getting hard to come by...

C


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