[JOKE] RPN vs. Algebraic: The Match !

[Valentin Albillo]

Hi, all:

[Caveat emptor: All that follows is thoroughly tongue-in-cheek, to try and cheer up the Forum a little. V.]

There's been a number of recent posts praising how RPN makes the process of evaluating an algebraical expression easy and intuitive, without having to deal with parentheses and/or implicit rules of precedence, etc.

Well, let's put it to test. Suppose we're asked to evaluate these
expressions:

    0.5 + 0.2 * 0.3 

and

    0.312 * 0.437 + 0.251

Here's how I would do it algebraically:

    Using the distributive property of addition over multiplication,

    also known as the distributive law of sum: a + b*c = (a+b)*(a+c):

       0.5 + 0.2 * 0.3 = 

                       = (0.5 + 0.2) * (0.5 + 0.3)

                       = 0.7 * 0.8 

                       = 0.56

    Similarly for the second one:

      0.312 * 0.437 + 0.251 =

                            = (0.312 + 0.251) * (0.437 + 0.251) 

                            = 0.563 * 0.688

                            = 0.387344

For a more complicated test, let's suppose we're asked to
evaluate the following expression:

   (2+1/4)^(3/2)

Here's how I would do it algebraically:

    Using the rule of exponents: (a+b)^c = c*(a+b):

       (2+1/4)^(3/2) = 

                     = (3/2) * (2+1/4) 

                     = (3/2) * (9/4)

                     = (3*9) / (2*4)

                     = 27/8 

What ? You don't like these algebraically obtained values of mine ? Well, let's see if RPN gets you any better results. :-)

Best regards from V.

Edited: 28 Mar 2006, 6:18 a.m.

[Namir]

This is an old PPC joke I heard over 20 years ago in one of the PPC national meetings. The joke is purely fictional.

The Santa Ana municipality issued a citation to Richard Nelson, founder of the PPC, for improperly disposing of trash bags! Richard was shocked because he did not improperly dispose of trash, pure and simple! It just was not in his character to do that! He drove to the municipality and confronted the official who issued the citation to protest against this error. “What crazy evidence led you to point the finger at me?!!”, protested Richard. The official calmly responded, “We found a fully functioning TI-59 calculator in the trash bag!”

Edited: 28 Mar 2006, 8:06 a.m.

[Palmer O. Hanson, Jr.]

Last month I broke down and purchased my first new-in-the-box High-Priced programmable calculator -- an hp-33s. I told Richard Nelson. Last week Richard told me that he had purchased a TI-89. Repent! The end of the world may be nearer than you think!

[Gene]

Yes, and I have seen that TI-89 in Richard's hands.

I have to admit I felt like sitting down quietly somewhere. :-)

[Namir]

This si truly shocking to me! I am emailing Dr Phil to help me deal with this trauma!

:-(

Namir

[Marcus von Cube, Germany]

Valentin,

let's try:

    0.5 + 0.2 * 0.3 

We have to transform the infix notation to postfix notation first:

    0.5 -> 0 5 .

    0.2 -> 0 2 .

    0.3 -> 0 3 .

The complete evaluation in RPN looks like the following:

0 ENTER 2 . 0 ENTER 3 . * 0 ENTER 5 . +    

which gives the result 5.00 accurate two 2 digits.

Marcus

[Howard Owen]

Typical sloppy RPN hackery.

The error is in the conversion to RPN. The digit string should be reversed, with the decimal staying put:

0.2 -> 2.0

0.3 -> 3.0

0.5 -> 5.0

Thus, algebraically we have:

5.0 + 2.0 * 3.0

and by the 2nd commutative law of addition:

5.0 + 3.0 * 2.0 + 6.4

or, in RPN:

2 ENTER 2 +

Which is five, purely by coincidence.

[Vieira, Luiz C. (Brazil)]

Indeed! (in the lack of a better word)

[Valentin Albillo]

Hi, Luiz Claudio:

Luiz Claudio posted:

"Indeed! (in the lack of a better word)"

It's "for lack of a better word" or "for lack of a better term".

By the way, congratulations for your fellow countryman Mr. Marcos Pontes becoming the first Brazilian cosmonaut ! :-)

Best regards from V.

[Vieira, Luiz C. (Brazil)]

Hi, Valentin;

Thanks! Twice! d8^)

Best regards.

Luiz (Brazil)