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RPN in primary education
Message #1 Posted by Chris Smith on 18 Mar 2013, 3:26 p.m.

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).

      
Re: RPN in primary education
Message #2 Posted by Walter B on 18 Mar 2013, 3:35 p.m.,
in response to message #1 by Chris Smith

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;-)

            
Re: RPN in primary education
Message #3 Posted by Chris Smith on 18 Mar 2013, 3:43 p.m.,
in response to message #2 by Walter B

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.

                  
Re: RPN in primary education
Message #4 Posted by Walter B on 18 Mar 2013, 3:46 p.m.,
in response to message #3 by Chris Smith

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:-)

                  
Re: RPN in primary education
Message #5 Posted by Dave Shaffer (Arizona) on 18 Mar 2013, 3:50 p.m.,
in response to message #3 by Chris Smith

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

                        
Re: RPN in primary education
Message #6 Posted by Manolo Sobrino on 18 Mar 2013, 4:43 p.m.,
in response to message #5 by Dave Shaffer (Arizona)

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.

                              
Re: RPN in primary education
Message #7 Posted by Chris Smith on 18 Mar 2013, 5:44 p.m.,
in response to message #6 by Manolo Sobrino

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.

                  
Re: RPN in primary education
Message #8 Posted by Jose Gonzalez Divasson on 18 Mar 2013, 6:37 p.m.,
in response to message #3 by Chris Smith

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

                        
Re: RPN in primary education
Message #9 Posted by BD on 18 Mar 2013, 10:22 p.m.,
in response to message #8 by Jose Gonzalez Divasson

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.

                              
Re: RPN in primary education
Message #10 Posted by Eddie W. Shore on 18 Mar 2013, 10:54 p.m.,
in response to message #9 by BD

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.

                              
Re: RPN in primary education
Message #11 Posted by Walter B on 19 Mar 2013, 2:14 a.m.,
in response to message #9 by BD

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:-)

      
Re: RPN in primary education
Message #12 Posted by Paul Townsend (UK) on 19 Mar 2013, 4:35 p.m.,
in response to message #1 by Chris Smith

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.

            
Re: RPN in primary education
Message #13 Posted by Thomas Klemm on 19 Mar 2013, 7:54 p.m.,
in response to message #12 by Paul Townsend (UK)

How I love taking square roots on my Odhner:

Cheers
Thomas

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

                  
Re: RPN in primary education
Message #14 Posted by Chris Smith on 20 Mar 2013, 5:48 a.m.,
in response to message #13 by Thomas Klemm

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.

                        
Re: RPN in primary education
Message #15 Posted by Thomas Klemm on 20 Mar 2013, 8:33 a.m.,
in response to message #14 by Chris Smith

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

                              
Re: RPN in primary education
Message #16 Posted by Chris Smith on 20 Mar 2013, 9:26 a.m.,
in response to message #15 by Thomas Klemm

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

Thanks for the information.

                                    
Re: RPN in primary education
Message #17 Posted by Thomas Klemm on 20 Mar 2013, 11:25 a.m.,
in response to message #16 by Chris Smith

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

                                          
Re: RPN in primary education
Message #18 Posted by Chris Smith on 20 Mar 2013, 5:02 p.m.,
in response to message #17 by Thomas Klemm

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 :)

                              
Re: RPN in primary education
Message #19 Posted by Mark Hardman on 20 Mar 2013, 8:38 p.m.,
in response to message #15 by Thomas Klemm

Here's an example on YouTube.

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

Mark Hardman

                                    
Re: RPN in primary education
Message #20 Posted by Thomas Klemm on 20 Mar 2013, 10:25 p.m.,
in response to message #19 by Mark Hardman

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

                                    
Re: RPN in primary education
Message #21 Posted by Paul Townsend (UK) on 25 Mar 2013, 5:14 p.m.,
in response to message #19 by Mark Hardman

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.

                              
Re: RPN in primary education
Message #22 Posted by Paul Townsend (UK) on 25 Mar 2013, 5:06 p.m.,
in response to message #15 by Thomas Klemm

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.

                                    
Re: RPN in primary education
Message #23 Posted by Thomas Klemm on 25 Mar 2013, 9:09 p.m.,
in response to message #22 by Paul Townsend (UK)

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.

                  
Re: RPN in primary education
Message #24 Posted by Paul Townsend (UK) on 27 Mar 2013, 5:00 p.m.,
in response to message #13 by Thomas Klemm

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

                        
Re: RPN in primary education
Message #25 Posted by Chris Smith on 27 Mar 2013, 5:43 p.m.,
in response to message #24 by Paul Townsend (UK)

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 :)

                        
Re: RPN in primary education
Message #26 Posted by Thomas Klemm on 27 Mar 2013, 6:33 p.m.,
in response to message #24 by Paul Townsend (UK)

You might like the CURTA SIMULATOR.

                              
Re: RPN in primary education
Message #27 Posted by bhtooefr on 28 Mar 2013, 8:46 a.m.,
in response to message #26 by Thomas Klemm

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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