RPN in primary education



#28

My 9 year old has been having problems with typical cheapy 4 op calculators for a few weeks at school (they've only just been introduced to them). Order of operations and suchlike don't work like they do on paper. She's pretty nippy on paper now. Stuck her on my 50g and gave 10 minutes of tuition on RPN and she's hooked and an hour later and she's flying through everything rather than wading.

They are allowed to bring in their own calculators. I wonder if the teacher will approve or not? (probably not).


#29

Do you have anything a little bit smaller than a 50G? A 30B will do as well IMHO and won't scare the teacher.

d;-)


#30

Unfortunately I only have a 50g to hand. A 30b is only £26 on amazon so perhaps that's an investment :)

I am slightly tempted to get a 35s but I'll probably steal it.


#31

Forget the 35S - not worth the Pounds IMHO. The 30B has a nice clean surface and won't distract your daughter by additional functions. And when she has made progress in some years as expected, you may convert it into a 34S.

d:-)

#32

How about a 33S - you may be less tempted, but she and her classmates may find it cool!


#33

The problem with four-bangers is that all of them are of immediate execution kind, the most unintuitive method ever. I don't think RPN is well suited for kids just learning the basics, I don't even think that calculators are good for them at such a young age. Infix notation keeping in sight not just the answer, but the expression to calculate i.e. mathematical display, formula calculators, EOS, V.P.A.M etc... are the way to go for kids checking answers without messing too much with their education... IMO. Sharp (e.g. 506, 531) Casio (991ES aka 115ES, 300ES 570ES, 82ES), Canon (e.g. 718), HP (e.g. 300s), TI (e.g. 30XS, 34) scientific operate this way.

Even if it is possible to use a scientific calculator at elementary school you should consider TI-15 Explorer, Casio FX-55PLUS (I like this one) and maybe TI-10. Anything above this just adds noise.


#34

I tried her on my FX 991ES but she spent too much time editing stuff - they're not that intuitive and are quite clunky.

Don't speak to me about the 300s - its a crime against humanity (its a cut down 991es type device on which the buttons don't work properly). I took mine in the garden and stamped on it after 2 months of miskeying. Horrid machine.

Agree about calculators as a whole but she's proven herself at arithmetic and now mechanical calculation plugging is a roadblock at learning other stuff I.e. getting stuff done.

#35

My children have 9 and 7. I have stored 2 HP15c LE for each for when they're ready for it.

This is a calculator that will not scare teachers, while can help them go through all of high school nicely (unless they are asked for CAS).

At this point in time, they couldn't care less for math calculations with machines. The younger wants the blue HP50g, but it's because it is beautiful (in a child way). Anything thrown at them would be a waste.

I look forward to teach them the beauty of saving keystrokes with RPN, and keeping the stack logic in one's mind. Or solving a repetitive problem with a small program (like when you're told to plot a function on millimeter paper). Probably this is best taught with a graphical calc, where all the stack is at sight; but that can create problems in class


#36

Quote:
My children have 9 and 7. I have stored 2 HP15c LE for each for when they're ready for it.

This is a calculator that will not scare teachers, while can help them go through all of high school nicely


And the 15C got me all the way through an engineering degree as well.

I don't know, and am curious, whether a 15C would be sufficient for an EE degree these days. Do today's courses REQUIRE graphing and extensive programming on handheld calculators?

It'll also be interesting to see if the 15C LE survives the years in storage, not being made quite as well as the originals were.


#37

Quote:


And the 15C got me all the way through an engineering degree as well.

I don't know, and am curious, whether a 15C would be sufficient for an EE degree these days. Do today's courses REQUIRE graphing and extensive programming on handheld calculators?

It'll also be interesting to see if the 15C LE survives the years in storage, not being made quite as well as the originals were.


I don't see why a 15C would not make it through an EE degree. A good friend of mine got his Masters degree in Math in 2011 (same year as me) and he had a TI-30XII.

#38

Quote:
I don't know, and am curious, whether a 15C would be sufficient for an EE degree these days. Do today's courses REQUIRE graphing and extensive programming on handheld calculators?

I don't see why a battleship should be required - after all the brains are going to be graduated, not the tools. Though an handy tool for quick on-the-fly calculations will help ...

d:-)

#39

If only they had been around 40-odd years ago when *I* was about eight years old. The best the school could do at that time was a hand-cranked "pinwheel" calculator - loaned to the school for a week. (It was another two years or so before the school actually bought one.) They let me loose on it as I was obviously the one who would best be able to use it. It could only really add and subtract. Multiplication was done by cranking multiple times then shifting one register against another to do the next digit. Even something as mundane as a square root was out of the question.

By the end of the week, I surprised the supplier by showing him how a square root could be done on the machine.


#40

How I love taking square roots on my Odhner:

Cheers

Thomas

Edited: 19 Mar 2013, 7:55 p.m.


#41

We had something that looked like that at school. Unfortunately we were never allowed to play with it.

How do you perform a square root on one of them? I can only think of Newton's method off hand if you're stuck with adding / shifting based multiplication.


#42

There are multiple methods of computing square roots but I'm using a digit by digit method. Actually it's the same algorithm as described in Cochran's patent that was used in the HP-35: Computing Square Roots

With Cochran's trick the method is similar to an ordinary division but you increase the divisor by 1 with each subtraction.

Kind regards

Thomas


#43

Interesting stuff and rather clever! I'll practice that on paper this evening.

Thanks for the information.


#44

Here's the list of operations when calculating the square root of 41:

Op     Register       Accumulator

41
* 5 205

205
- 5 200
- 15 185
- 25 160
- 35 125
- 45 80
- 55 25
- 65 -40
+ 65 25

2500
- 605 1895
- 615 1280
- 625 655
- 635 20
- 645 -625
+ 645 20

2000
- 6405 -4405
+ 6405 2000

200000
- 64005 135995
- 64015 71980
- 64025 7955
- 64035 -56080
+ 64035 7955

795500
- 640305 155195
- 640315 -485120
+ 640315 155195

15519500
- 6403105 9116395
- 6403115 2713280
- 6403125 -3689845
+ 6403125 2713280

271328000
- 64031205 207296795
- 64031215 143265580
- 64031225 79234355
- 64031235 15203120
- 64031245 -48828125
+ 64031245 15203120

1520312000
- 640312405 879999595
- 640312415 239687180
- 640312425 -400625245
+ 640312425 239687180

The subtraction is repeated until the bell rings because the accumulator is negative. Then the last revolution of the crank handle is reversed. The square root can then be found in the revolution or quotient register.

Have a nice evening

Thomas


#45

That's a rather clever way of solving it. Thanks for the explanation - much appreciated

Attempting to write a rather naive RPL version of the algorithm now (my paper version became tedious very quickly :)

#46

Here's an example on YouTube.

Extracting Square Root on the Original-Odhner Model 227 (1:36)

Mark Hardman


#47

Nice finding! Töpler's method is slightly different as the multiplication by 5 is not used. Thus the register has to be incremented by 2 instead of 1. This may lead to a carry to the next digit, as can be seen with the digit 8 of the result.

For comparison here's the calculation of the square root of 125 with Cochran's method:

                             125

* 5 625

625
- 500 125
- 1500 -1375
+ 1500 125

12500
- 10500 2000
- 11500 -9500
+ 11500 2000

200000
- 110500 89500
- 111500 -22000
+ 111500 89500

8950000
- 1110500 7839500
- 1111500 6728000
- 1112500 5615500
- 1113500 4502000
- 1114500 3387500
- 1115500 2272000
- 1116500 1155500
- 1117500 38000
- 1118500 -1080500
+ 1118500 38000

3800000
- 11180500 -7380500
+ 11180500 3800000

380000000
- 111800500 268199500
- 111801500 156398000
- 111802500 44595500
- 111803500 -67208000
+ 111803500 44595500

4459550000
- 1118030500 3341519500
- 1118031500 2223488000
- 1118032500 1105455500
- 1118033500 -12578000
+ 1118033500 1105455500

110545550000
- 11180330500 99365219500
- 11180331500 88184888000
- 11180332500 77004555500
- 11180333500 65824222000
- 11180334500 54643887500
- 11180335500 43463552000
- 11180336500 32283215500
- 11180337500 21102878000
- 11180338500 9922539500
- 11180339500 -1257800000
+ 11180339500 9922539500

Kind regards

Thomas

#48

My procedure exactly. It might be easier to watch this than to read my explanation below. OK so I wasn't the first to work it out, but the guy who came to collect the machine at the end of the week was clearly impressed by the 8-year-old me who had worked it out - and could even explain why it worked.

#49

That picture brings back memories! The machine we had in school looked a bit more modern than that (1960's model no doubt), but the registers were all the same size (10 digit input register, 8 digit counter, 13 digit accumulator) and the internal works were quite likely unchanged.

My procedure relied on the identity 1 + 3 + 5 + 7 + . . . + (2n-1) = n^2 (which I had discovered for myself at the age of about six) so that consecutive *odd* numbers were subtracted each time until one was found that "didn't go". Let us find the square root of 10. We begin with 10(.)00000000 in the accumulator, and clear the counter. Begin with 01(.)00000000 in the input register, and subtract. Then change it to 04(.)000000 and subtract again, etc.

You find that the subtraction of 07(.)000000 "doesn't go" (the bell rings and the accumulator reads 999.....) so you undo it, reduce the input register by *one* (to 06(.)000000), shift the carriage one place left, enter a new 1 into the input register (so it now reads 61) and start subtracting again. The subtraction of 61..... goes, the next one of 63..... does not. So reduce it to 62....., shift one place left again, and insert a new 1 to make 621...... and continue as before. This position survives six operations, up to 631..... (633..... doesn't go).

Etc. etc.

In this way the square root builds up, digit by digit, in the counter register, and the accumulator gets reduced to as near zero as possible. (The input register tends to end up at nearly double the actual square root - why?)

Edited: 25 Mar 2013, 5:07 p.m.


#50

Quote:
The input register tends to end up at nearly double the actual square root - why?

It's all because of: (x + d)2 = x2 + 2xd + d2

Here x is the actual guess while d is the next digit and we're trying to get close to 10 in your example.
And that's where you can see the benefit of Cochran's trick: by multiplying the whole equation by 5 the input register will keep 10x instead of 2x.
But that's the same as x, only shifted by one digit to the left. Thus the input register and the revolution register end up with the same number (upon the additional last digit of the input register which is 5). That's why only one register was needed to keep the result in the HP-35.


Those of you having an iPhone may install rpn-21 which provides a debugger:

Just enter 125, then the blue shift key and double tap the display to enter the debugger. There you [press key ...] which brings you back to the calculator. Now press [chs] (which is where to find the square root) and hit [run]. After a while you should be able to follow the calculations in the registers a and c with the help of the listing in my message #20 above.

Here are the lines corresponding to the screen shot of the debugger:

                            8950000
- 1110500 7839500
- 1111500 6728000
- 1112500 5615500
- 1113500 4502000
- 1114500 3387500
- 1115500 2272000
- 1116500 1155500
- 1117500 38000
- 1118500 -1080500
+ 1118500 38000

The main loop to calculate the square root are these three lines:

0833: c + 1 -> c[p]
0834: a - c -> a[w]
0835: go to 833

Kind regards

Thomas

Edited: 25 Mar 2013, 9:27 p.m.

#51

Has anybody written an emulator for one of these hand-crank mechanical machines?


#52

I actually considered that and had a look around but couldn't see anything. Might have a go if i get the time as I've got a week of holiday soon :)

#53

You might like the CURTA SIMULATOR.


#54

And on that topic, the winning entry of HackFest 2012 (a programming competition at KansasFest, an annual Apple II convention, in which the entire project is written, beginning to end, at the event) was a Curta simulator for the Apple II.


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