Reverse polish notation is really related to tree traversal algorithms. If you build a tree whose nodes are operations and its leaves are the numbers (or variables), you can express any calculation you like. If you read the tree in post order, you get the reverse polish notation equivalent of that. If you use pre order or in order, you get polish notation and traditional notation, respectively.


Building the tree for (3+4)*5-2 gives us a tree like this one:

(-) - (2) 
(*) - (5)
(+) - (4)

I know it's an awful way to draw a tree... my excuses...

Inorder traversal gives us 3+4*5-2
Preorder traversal is - * + 3 4 5 2
Postorder traversal 3 4 + 5 * 2 -

Of course, with inorder, you need parenthesis in order to avoid ambiguity, but you don't need them with reverse polish notation.

This was also used in the venerable Forth programming language.