Why RPN?


OK, perhaps I'm just an ignorant student who's been lulled into the security of using algebraic calculators, but I think I have a legitimate question that others may benefit from.

One of the key selling points for HP versus other companies among communities like this seems to be RPN. Why is it considered so much better? I have seen that you can make the same calculation in less key strokes than in an algebraic mode. So, it saves memory in programs, providing more room for other programs, and may even save a few seconds in solving a problem during an exam. But honestly, in these days with cheap memory, is that really that important? What other benefits does RPN provide that you can't get from an algebraic calculator?

Here's another question: I'm betting that RPN is exclusive to HP for a reason, perhaps something related to copyrights or patents. But if another company were able to produce an RPN calculator, say TI, would people in this community take it seriously? Or do we just hold on to HP calculators out of nostalgia or something like that?

I think you can see my confusion, anyway. I've followed some of the threads here, and it seems to me that there's a real demand for a powerful scientific calculator out there that's just not being provided for. I know I'd love to have this "dream calculator", and I keep hoping perhaps a group of people could make a case to any of the companies (either HP or TI or anything else, for that matter) to produce that calculator. Maybe someday. Who knows, maybe this hydrix calculator I've heard about might become what we're looking for.

Edited: 26 May 2004, 2:09 p.m.


Do this on pencil and paper:

+ 3

- 3

* 6

Now try it on an RPN calculator like 42

Edited: 26 May 2004, 2:21 p.m.



Try it this way, too:

on a 20s:

2 + 3 =
9 - 3 =
* <LAST> =

or on a 33s ALG:

2 + 3 <ENTER>
9 - 3 <ENTER>
* X<>Y <ENTER>

(Notice that the 20s is actually more natural and versatile than the 33s ALG system here---you can start a 2nd calc chain without having planned to, and still go back and bring in the last chain result. Not so with the 33s, where if you don't consciously swap the 1st chain result back to the background ["y"] you will lose it).

(But I agree with you, the RPN is so much mre natural and elegant and *exactly* like on paper!)




Because.. (;-)

none of my other friends work from the inside (to) out.

who wants to have to remember Order-of-Operations (Precedence) anyway?

I just want the answer, I don't care how it got it.

I don't care if intermediate results seem reasonable or not.

if I make a mistake, I can just start over again.

Sorry. I was just reacting to the attitude of a new college-grad Industrial Engineer that told me he couldn't stand HP calculators because of that "reverse entry stuff".



You say an argument for algebraic is so you don't have to remember order of operations--but remember that not all algebraic calculators are like graphing calculators. Take any simple, non-graphing, single line calculator, especially one without parentheses on it. Order of operations is still required to get the right answer on these calculators.

Perhaps one benefit to algebraic entry is that it more naturally matches what people learn to do in math--you think about the entry in the same way you think about the algebra. For many people, it can be hard to keep track of where in the stack everything is, and an algebraic system seems more intuitive to them.


Gabe wrote:

Take any simple, non-graphing, single line calculator, especially one without parentheses on it. Order of operations is still required to get the right answer on these calculators.

Aha! You said it, right there.. "without parentheses"! That's the whole point we've been trying to make: Parentheses, who needs 'em? Or to borrow from an old song: Parentheses, what they good for.. absolutely nuthin'!

Gabe later said:

For many people, it can be hard to keep track of where in the stack everything is, and an algebraic system seems more intuitive to them.

Au contraire mon frere (please excuse my French :-)! Using that same simple, non-graphing, single line calculator, let's assume it has one memory location (i.e. register). An equivalent simple RPN calculator can be viewed as having multiple automatic, albeit temporary, memory registers (i.e. stack).

On an RPN calculator, once you're finished with the first calculation, you just start working on the next (second) part of the expression. The first result will simply be bumped up a level. No need to Store it anywhere. When the second calculation is finished, guess what? The first result is right there waiting for an operator to be pressed that will "operate" on the first and second results. No need to Recall the first result from memory.

Isn't that simple? Isn't that intuitive? If a person were to learn this (RPN/stack) methodology as a youngster, I believe later exposure to algebraic entry would be seen as being counter-intuitive (less efficient). This person might say "You're telling me I have to store intermediate results manually? Why? My HP does it automatically."

If you're unsure of what's currently on-the-stack, it's easy to Roll the stack to view each of the four registers. It's also easy to exchange (Swap) values in different registers. In other words, it's not hard to keep track of what's on the stack.

Finally, to learn how to use an RPN/stack-oriented calculator, I feel a person needs to be open-minded enough to unlearn (or temporarily let go of) Algebraic-entry long enough to see the merits of a different way of calculating expressions. In doing so, a person might very well come-out saying "Hey, this is a better, more efficient way". At least that's what I found.



I've several brochures in which RPN is explained with benefits as less key strokes, so efficient and fast to get results.

My opinion is that the threshold to get used to RPN is somewhat higher than for "normal" systems and after this, much is a matter of personal preference. Also, I think that any system can be justified with a specific example that precisely that system handles best.

So what then is the real advantage? It is mentioned in the brochures, though never as first one: error correction. I must admit, it's not a good one to start with but unless you'll never make any mistakes, this is where RPN proves its value.
In algebraic systems you better start all over when making a typing error like pressing a number before an operator (previous number will be lost) or pressing the wrong operator (cannot always be overwritten by the correct one without wrongly performing part of the computation). A mistake can easily be reversed in RPN. With RPN you just feel that you're in control over what you're doing.

If possible, give it a try, and you'll be convinced.



Yo uare absolutely right. I have used "LASTx" countless times over the years in order to correct mistakes in entry---it is a really important point---and you are right.

Indeed, that is the beauty of RPN, it is a totally efficient, logical and consistent entry system for carrying out computations---and it is way more "natural" than algebraic for on-the-fly work---precisly for the reasons you mention: since the operator is LAST, you can be sure EVERY TIME that you are sure of what the operator is doing---you can even review with SWPA just before! And if you lose your train of thought, you can check LASTx to see where you had been (and then clear it out--sometimes this will mess thing up if you are using the whole stack, though).




I have used both over the last 30 years. It depends a little on the implementation. HP 27S, one of the few classical algebraic HP machines, has such a great implementation that I like it a lot. Here I found the "9-3" example not so convincing.

When calculating expressions with many nested brackets and functions however, you really will love RPN. You can not use different type of brackets and it is just too easy to get lost....and than you start the calculation over again. Never a problem with RPN.

Jan (CH)


I too was an ignorant undergrad, back in the early '80s. Luckily for me, my TI-55 was stolen, and I bought an HP-15C to replace it. Haven't been back to algebraic since. Once I got used to RPN, I said, "Gee, why did I wait so long?"

I personally have HP RPN calculators for daily use. I also have the nagging fear of someday not having one if my modest collection starts going Tango Uniform, so I keep an eye out for units in decent working condition. I can't afford mint!

As to RPN itself, there are other non-HP RPN calculators out there - various Novus/National Semiconductor and Soviet models are probably the easiest to find. However, IMHO they aren't nearly as well made, nor as functional, as classic HPs.


How about because it's much easier and more intuitive to work with RPN caculators than with "algebraic" calculators?



Lots of great replies so far. First I point you to the first page in what I plan to make several pages of an RPN How To.

Also keep in mind that RPN isn't the only reason most people here prefer HP. In the past HP has always had a much higher quality machine. The keyboard feel and layout more well thought out than most if not all other calculators.

There are Russian made RPN calculators and I think one other brand made in the USA. Also math coprocessors all use RPN because it is the most natural way to do it for a computer too.

My final reason and I think the best reason is this. I was taking a test one day that relied heavily on complex calculations. Calculations that you couldn't program in a head of time. Keep in mind that while I generally know the material on a test better than most people I am a slower test taker than most. On that test I was finished long before anyone else in the class was. The only reason I was done first is because of my RPN calculator.


I like RPN because:

-Error correction

-It shows intermmediate results!

-Don´t need of parentesis (less keys/no mental parentesis count)

-I feel that it´s less probable to make a mistake

For a smart programmable system like HP-41C:
You can write code that acts exactly like built in functions. For example you can redefine all the math functions to work with complex numbers or with fractions or (as I did) with numbers that have an associated error; and asign the new functions to the original keys. Its easy to do: the programs take the values from the stack and return the results to the stack. Easy, Beautiful, Smart.

Two RPN calculators where made in my country (Argentina) in the ´70s. See www.calculators.com.ar



We RPN fans always have to justify why we like RPN. Let's turn the tables... "Why Algebraic?" We have all heard the advantages of RPN over algebraic, but surely there must be some advantages to using Algebraic Entry (after all, so many people use it)

Here is what I see as being possible advantages for Algebraic. You can essentially "copy-paste" from a math problem. It doesn't require you to think much at all (and consequently, the resulting information is less powerful (no intermediate results) and more complicated to enter (using parentheses)

It is kind of like the battle between those who make websites by programming and those who use a WYSIWYG (what you see is what you get) environment. It is considerably easier to design something in WYSIWYG provided it is simple. It gets much more complicated in some cases (when adding several frames and tables) to use WYIWYG. With WYSIWYG, you also have lower quality sites, with more wasted space (innefficient code)

Essentially Algebraic entry is taught in our schools because anyone can do it. A monkey could be trained to use an algebraic calculator (if you see an open parentheses, press open parentheses). RPN requires thought, but essentially is more intuitive than algebraic mode (you get 2 pieces of information and then decide what to do with them).

After the short learning curve, RPN makes much more sense than Algebraic. If you are doing extremely complicated math problems for the sole reason to do extremely complicated math problems (like if you are just doing arithmetic), then RPN is the only choice. Let me give you an example.

Download this file: http://texasmath.org/DL/CA03C.pdf
It contains a UIL (University Interscholastic League) Calculator test. 99% of the people taking this test use a HP 32sii. Go to about the 5th page of the problems (or even the second page). In sheer number of keystrokes, RPN could finish either of these pages almost twice as fast as an algebraic calculator. This does not even include the extra thinking involved for algebraic (have I closed that parenthese yet... did I store that value in mem 1 or 2?!?)

Just my thoughts. Give it a try... I have used both RPN and Algebraic and I will give you 2 guesses as to which I use now (and which I like better). I won't be going back anytime soon (I am starting to sound like an "Apple Switch" commercial)

-Ben Salinas
11th grade


Whoa. What are the non-calculator tests like?

Why would there be a competition involving the ability to do rote calculations, which is what that test you linked to is?

Are there ones that test math ability?


There are tests in many subject areas (the mathematical related ones: Science (a test covering biology, chemistry and physics), Math (a test covering algebra 2-Calculus), Calculator (as shown there), Computer Science (in Java), Number Sense (mental math... you may not have any scratch work, only the answer)). There are also literary events (spelling, literary critism, etc), but I don't do those.

The calculator test is really a silly one, but in preparing for it I have learned how to use my calcualtor lightning fast (helpful for the other events) and since I started using the 32sii for the UIl tests, I took it one step further and learned every feature on my calculator. The math test is a good test (decent). Some of it is knowing short-cuts, but they are shortcuts that are somewhat helpful in real life. It's a lot of word problems.

The Science test measures information in all 3 subjects. The biology section is mainly trivia, and about 1/8 of the physics and chemistry sections are each trivia also.

The computer science test is worthless (in my opinion). It does not test how well you can program, or how well you know theory even. It tests if you can make pretty messages print out (i.e: "What does System.out.println("\t\\\"THIS");), or if you can find errors. Our school has a decent computer science program (we can write some fairly complicated programs that work) but we don't do well on these tests.

Hmm this rant is getting a bit long.

Basically the UIL tests, at least for me, acted as an introduction to new math topics, new calculators (with UIL, I would not be posting here... I would be doing my homework with my TI-30xa... ughh), provides a way for me to keep my old math and science in practice

But yes, the calculator test is pretty pointless (we sometimes refer to it was "monkey" practice (calculator practice))




Why would there be a competition involving the ability to do rote calculations, which is what that test you linked to is?

Texas has long been famous for competitions that measure the speed, agility and accuracy with which contestants can perform calculations, rather than the ability to determine how to solve problems (there are other competitions for problem-solving). Before calculators came along these competitions were held with slide rules. The contests were so popular that one of the major slide rule manufacturers, Pickett, came out with a model designed especially for competition. The Texas Speed Rule had scale layouts designed to make chain calculations as efficient as possible by limiting the amount of slide and cursor movement necessary. (Saving a second or two on a long calculation could make the difference between winning and losing.)


Ben Salinas wrote:

It doesn't require you to think much at all (and consequently, the resulting information is less powerful (no intermediate results) and more complicated to enter (using parentheses)

Um, you threw me completely, there, Ben. There's an unmatched parenthesis in that sentence.


--- Les Bell [http://www.lesbell.com.au]


Be it mathematics, or English :^)

(You'll find a lot of missing parens in my writings here, too!


Except that if you use a HP calc, it fills the closing paranthesis for you (unlike the stupid TI All-Get-Brains calculators)


I started with the TI-58c (with AOS, not RPN) and liked it a lot. It kind of bugged me that the RPN ads would give misleading examples about how much more efficient RPN was. They would show some complex calculation that ended with half a dozen sets of parentheses to close, if you could remember how many you had open. In the TI's AOS, you could close them all at once by pressing the = key.

When I got the HP-41cx and began doing far more than calculations with it-- file operations, using it as a controller for electronic instrumentation, etc.-- RPN suddenly was not just another way to do it, but was clearly superior.

As for programming, RPN does make for cleaner parameter-passing for subroutines and so on, but it would have been nice to have a stack of more than just the four positions that we inherited from the days before calculators were programmable or could handle really complex programs.


If you are in an H-P site you can expect to see mostly material that tells you why RPN is better than algebraic (AOS). It's a lot like going to a Chevy dealer and asking him if Chevvies are really better than Fords.

Many years ago in the heyday of the HP-67 and HP-97 the H-P folks came up with a Mach Number calculation that they believed showed the advantages of RPN over AOS. They were so sure of it that the equation was on the cover of the manuals for those devices. But, for another view you should go to www.woz.org/letters/general/57.html and read to the end to find a description of using an AOS machine by Bill Wozniak, the co-inventor of the Apple computer:

"... At Hewlett Packard we were so proud that our calculators, the first scientific ones ever, were years ahead of competition. They used postfix partly because the least logic or ROM chips were quite expensive back then. It would have taken extra keys and an infix to postfix translator to use infix. Also, a larger and more expensive desktop HP machine from the division in Colorado Springs used postfix, for the same reasons. The HP-35 was an attempt to miniaturize this machine.

Our marketing department had a card with a monstrous formula to demonstrate how powerful our calculators were and what postfix calculation was capable of. They challenged people to solve it on a slide rule the normal way. Well, we could all solve it on our HP calculators but it took a few tries to get the steps accurate enough, there were so many of them.

Finally Texas Instruments introduced an infix 'algebraic entry' scientific calculator. The first one showed up in our lab one day. We were all pooh-poohing it and laughing at the arithmetic entry as being too weak for engineers. Someone pulled out our big formula challenge and we all laughed, sure that nobody could ever do it with the TI calculator. A challenge went up for someone to try. After a short silence I said that I'd try.

Well I started staring at the formula and looking at the keys and trying to decide which steps to calculate first, as you would do with an HP calculator. I finally realized that I'd never be able to solve the formula this way. With my fellow engineers watching I was very self conscious but I wanted to succeed. I managed to let go of my thinking and then came up with a very amazing concept. I just copied the formula from left to right! This was such an incredible concept that I pressed the keys as fast as I could on the TI calculator, risking a wrong press but impressing my colleagues. I had to guess whether this calculator used the square root button as prefix or postfix but I guessed right and got the proper answer the first time.

My colleagues couldn't believe it. I told them that you just copy the formula from left to right but not one of them could see through their postfix fog. After all, these were the calculator experts of the world. They are well accustomed to thinking ahead and analyzing an expression to come up with the order of steps to take on an HP postfix calculator, and they had to remember which sub-expressions were in what order on the calculator's stack. None of them could do what I had done, forget that they have to be smart."

One of the curious aspects of the selection of the Mach Number calculation to demonstrate the superiority of RPN over AOS was that the problem was exactly of the level of difficulty which allowed it to be easily performed by the least capable machine in the TI inventory at that time, the TI30!


The mach number formula and RPN vs. ALG entry was treated in great depth in the following thread. You might find it of some interest.


Mark Hardman

Lobotomozed C++ Programmer

Houston, TX


Once I was part of a "competition" between HP and TI. I was one of very few persons to have an HP-21, and many times I had discussions with fellow students, who owned a TI-53 (if I recall the number well). Neither one could convince the other to have the better machine on a theoretical basis, but in real life (well, perhaps you wouldn't consider the "lab" a real world, but that's another discussion. For calculating it surely was) my 21 proved to be a nicer companion. True, the TI had more functions, memories and decimals, but my results appeared sooner, easier and mostly first time right.

The HP-21 has only 1 memory, but I hardly ever needed it in a computation. Sometimes, to hold a result for later use in a different computation. The TI-ers almost always needed 1 or 2 memories.

What I DID notice during these "fights" was that a taller stack could have meant an improvement. I discovered after some time that the 4 levels were just the right number when working from inside out; more aren't required. Would you have more levels you could also work from left to right. For example, the Mach number needs 5 levels, in case you insist on starting with the number 5 right inside the squareroot function.

It was only a thought; I never really have desired to have more levels.


Phwoar! The Mach Number calculation is trivial, provided you have the right tool, which can solve it in just a few seconds:


There are times when a whizz wheel is simpler and faster.


--- Les Bell [http://www.lesbell.com.au]


Just for reference here is what we are talking about.

From reading this

Our marketing department had a card with a monstrous formula to demonstrate how powerful our calculators were and what postfix calculation was capable of.

and this

Well I started staring at the formula and looking at the keys and trying to decide which steps to calculate first, as you would do with an HP calculator.

I was expecting something much more complex than that. You don't even need the full 4 levels of the stack to calculate that.

Steps as performed on an HP 15C

661.5 /
2 y^x
.2 *
1 +
3.5 y^x
1 -
6.875 EEX 6 CHS ENTER (First time 3 levels are needed.)
25500 *
1 x<>y (that's x y exchange)
5.2656 CHS y^x (back to only 2 levels being used.)
1 +
.286 y^x
1 -
5 *
answer: 0.8357

Maybe I have been using RPN for too long but that was easy, was very natural, and took almost no thought.

Chris W


Even on that one, you could go left to right with RPN-- it would just take more stack levels.


Esteemed Student: Other people have put forth some good answers to your question. Mine is that while i don't know why; back in the "golden age" of calculators (when people had to think to get a numerical answer) serious users chose RPN. Some smart folks and good programmers used others like the TI 58/59 but not as many. Fewer yet are still being used.

Doug and Chris: There are more RPNs than that. If you are interested you can see my collection at http://www.msdsite.com/forums/upload.php?upload=view&uid=482

Chris: I didn't know that. Coprocessors rule!!!!!!!!!

Guillermo: Que increible la Czerweny! Tiene un extra? Quieres intercambiar RPNes?


Dear Student,

I just KNEW you'd get many, many reactions, but has your question been aswered?

I wonder.

I happen to have recently scanned the brochure "Enter vs. =" by HP. I guess you can guess what it is about. I still must ask HP if they mind my violation of copyright, but if they don't I could send it to you, if you like.


Yes, I have learned a lot. It seems that the arguments are the same, but at the same time those arguments seem to have more validity. What it seems like to me is that the only way to find out whether or not RPN is better for you is to try it. Which means either blowing $50 on what could potentially not be the calculator you want, or else to borrow someone else's. I don't know anyone who uses one, unfotunately, at least that would let me take it for an extended period of time.

That's probably one of the main arguments algebraic users have against switching--the cost. Anyone know of a good way to expose someone to a fully functional RPN calculator without having to commit to spending lots of money?


There are a pile of windows emulators: I'll send some of them to you right now:




Yeah, $50 is what it takes, but you can buy a lot for $50.

ie You could buy an Hp28s, Hp48G or a new HP33s. And if you are not tied to the scientific line, an Hp12c or an Hp17Bii can all be purchased for about that amount or less via ebay.

An Hp33s isn't bad (actually the best non-graphics calculator available, new). An Hp48G is also a good buy for what you would get. The new Hp48GII (which is really an Hp49G minus) can be found on the web for $80 plus S&H. That makes it the best bargain out there esp compared to the Ti line for price to features. And the new Hp's can always be set into the algebraic mode should you not like RPN (hard to believe, but some people NEVER learn to like or appreciate, period.).


Some hear have eluded that while RPN is clearly more efficient, it is more difficult to use and requires more thought to figure out how to proceed. An example was given as difficult to solve in RPN, and easier, although requiring more key strokes using algebraic entry. I strongly disagree. If you do nothing more that add a list of numbers it is a tie as far as efficiency goes. If you do anything more complicated RPN is more efficient, natural and easier. I will concede that it may be possible to write an equation that would be more difficult in RPN, but I have never seen one, and I challenge anyone to give me a real world example of one. If you insist on using both algebraic and RPN, I can see where some might think that RPN requires a lot of thought. If you decide to give RPN a try I strongly recommend that you put your algebraic calculator in some place that is very difficult to get to, and don't even think about it for a week or so. If you are using RPN multiple times a day, one week is more than enough to make you realize that RPN is in reality better than algebraic entry for performing calculations. If you are looking for an in expensive way to try RPN, and you can live with doing it at a computer, I would recommend one of the emulators, V41 is one I like. It is easy to install, has skins of different sizes so it runs well at various different screen resolutions. The 41 is a good one to learn on because it is one with a 4 level stack and once you learn on a 4 level stack the newer ones that have an unlimited stack are easy to pick up. Going the other way is not as easy. I have a short intro to RPN on my sight you may want to look at too. I plan on expanding it some time soon. So take a look at this page.
RPN How To


Anything requiring more than 4 levels of stack is more complicated:
A) You may loose the top level unnoticed
B) You need to do STOre and ReCalL
C) You may not remember the right point for RCL
D) Many stack levels makes it hard to do manipulation
E) New commands like FILL (shift ENTER) are needed
F) ...


Ah, but now you're thinking of just one equation done by hand. Think of a program where you're using let's say 3 levels on the stack, and you want to run a subroutine to get the next number to work with. Let's say that subroutine needs 3 levels as well, and futher, that subroutine calls another one that needs 2 or 3 or 4, etc.. As you're programming, you don't have to care what's beyond the few levels you're working with at the moment. Each routine is concerned with only its few stack levels, even if there are 23 other things on the stack below. It doesn't matter. You won't get confused. We do this in Forth all the time, and most things work the first time we try them, unlike the case with other languages. Stack comments in the code only mention the few things that are relevant to the particular routine, regardless of what else uses that routine and leaves other numbers pending on the stack. The maximum stack depth is deep enough that we never have to worry about overflowing it.


I used algebraic entry for years and was hooked on RPN the first time I tried it. For me the implications of the entry method were immediately clear, and I still seem to be hooked on it ;-)

There are several reasons I think people refer to RPN as "too hard." Humans are lazy animals and creatures of habit. Once you learn to do something, even if it's not the most efficient way, you will typically have a hard time changing. The other problem is that most people only carry out very simple math operations... so the efficiency of RPN vs. algebraic is basically equal. That makes for a hard sale.

Most engineering/science students these days avoid RPN. If only they knew those parentheses could be avoided...

Best Regards,
Hugh Evans


One easy way to realize the advantages of RPN is to ask yourself a very simple question: what are the “rules” for using an algebraic calculator? For example, what actually happens when you press the + key?

Well, depending on the circumstances, pushing the + key can perform a wide variety of arithmetic operations. These include subtraction (example: 5 – 3 +), or multiplication (5 * 3 +), or division (5 / 3 +), or exponentiation (5 ^ 3 +). Sometimes the + key even performs addition (example: 5 + 3 +; the second push of the + key performs an addition, although the first does not).

In other circumstances, pushing the + key does not perform any arithmetic operation. It simply sets up a pending addition, which may be performed later when the = key is pressed (5 + 3 =), or in some cases by a right parentheses (5 + 3), or in some cases by a second push of the + key (5 + 3 +), or in some cases by the subtraction key (5 + 3 -). In other cases, subsequent presses of the right parentheses, + and – keys may not perform the pending addition, depending on the configuration of parentheses; for example 5 + (3 + 4 – 2) will not perform the first addition.

The same rules also apply to the – key. However, the rules are different for the * and / keys, and they are different again for the y^x key. Also, the rules may be different for unary operations like cos or log; on many algebraic calcs, unary operations are performed immediately, and are not affected by the = key, or by parentheses, or by any other operations.

Now read through all that again. Is it correct? Doesn’t it seem just a bit complicated when you think about it?

Now let’s consider the rules for an RPN calculator. They may be summarized as follows:

Pushing the + key immediately performs an addition. All other operator keys behave in the same way.

OK, that's it. Any questions? Would it be fair to suggest that the RPN rules are simpler?

Edited: 28 May 2004, 12:46 p.m. after one or more responses were posted


Beautifully put, Norris.

Calculating sin(pi/4) makes an excellent demonstration of the inconsistency of many algebraic calculators, methinks.


--- Les Bell [http://www.lesbell.com.au]



That was the best explanation of RPN over ALG I have seen in this "thread" so far; possibly the best I have ever read/heard.

I threw away a malfunctioning algabraic calculator (threw it out a dorm window, actually) more than 20 years ago. I got an 11C because I liked the way it looked, the way it was laid out and its "heft" and "feel". Also, a couple friends had been going on about how great RPN calculators were. I practiced RPN until I could use it efficiently (it took about two days) and I have never looked back. RPN "logic" just seemed so incredibly intuitive (it still does, by the way). I've never tried to figure out WHY before, but your explanation sums it up pretty darned well.

Take care.



I would like a copy if possible.



I've held off giving my answer, but no-one else has suggested this, so here goes:

RPN is better than algebraic because it clearly mirrors the mental model one would use when performing arithmetic calculations. This is what people are getting at when they say it models the way you would perform addition, etc. on a piece of paper. It is easy to visualise what's on the stack, and there's no hidden "state" information for the user to keep track of - at any time, you can take what's in the stack and use it in a calculation, change direction, think about things for a moment and then resume, etc. The calculator and the mental processes are in tune, and in step.

An algebraic calculator has a stack, too - but it's hidden from you and manipulated indirectly via arithmetic precendence rules and use of ( and ) keys. It's difficult to know exactly what's in that stack and what operations are pending, and you can't easily do things like saving intermediate results for re-use the way you can with RPN.

In addition, algebraic calcs often have strange inconsistencies like relying on an M+ operator rather than simple STO and RCL operations. I've tried to use my son's school-issued Casio calc, but it's just weird and makes no sense to me.

Algebraic notation is the way we all learn to perform symbolic manipulations, and so perhaps it has a place in educational graphing calculators which do that kind of thing. But it's not the way we do arithmetic, whether in our heads, on the back of an envelope, on a spreadsheet or on a real calculator, which - of course - uses RPN.


--- Les Bell [http://www.lesbell.com.au]

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