RPN stands for "Reverse Polish Notation," a
parenthesis-free method for performing calculations. In
the United States this method has been popularized by the Hewlett-Packard Corporation1,
which sells a line of RPN calculators. The method depends
on a stack of values as its organizing principle. When a
number is entered, the previous entry is
"raised" in the stack, so that several values
can be stored. When a mathematical operation is
performed, it is performed on the most recent value (or
values, if more than one is required).
For example, to divide 80 by 81, you make these
entries:
80
[Enter]
81
/
At first, this method may seem cumbersome, but in time
one begins to see its great value — one need never worry
about algebraic order of precedence, because the order in
which operations are performed is entirely controlled by
the order in which the values are entered and the
operations performed.
On some problems, the algebraic order of precedence
can be depended on to provide the correct result. But
many problems are difficult to state using the default
precedence. In this next example, you want to multiply
the result of two additions ((a + b ) * (c + d)). If you
simply enter this problem into an algebraic calculator,
you will get a + (b * c) + d, not (a + b) * (c + d), as
you expected, because multiplications are performed
before additions.
In order to solve this problem on an algebraic
calculator, you must carefully place parentheses between
the operations (assuming your calculator has
parentheses). But in RPN notation, the problem is simple
to solve:
a (vaue)
[Enter]
b (value)
+
c (value)
[Enter]
d (value)
+
*
Once you begin to get a feel for RPN, you will realize
it is the easiest way to solve all but the simplest
problems. You never have to press more keys than on an
algebraic calculator, and you often press far fewer.
(1) The name Hewlett-Packard is a
registered trademark of Hewlett-Packard Corporation.
Hewlett-Packard in no way endorses or is affiliated with
arachnoid.com. I just like their products.
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