Multiplication Signs

Date: 10/07/2002 at 21:12:13
From: Amy W.
Subject: Multiplication signs

Why are there four different ways to indicate the operation of 
multiplying?  x, parenthesis, dot, and numbers beside each other? I 
think x can't always be used because sometimes it's a variable in an 
equation. I don't know why all these ways mean multiplication.

Date: 10/07/2002 at 23:18:51
From: Doctor Peterson
Subject: Re: Multiplication signs

Hi, Amy.

The different symbols arose through history, and although each new 
symbol filled a need, the old symbols still had advantages in some 
circumstances, so they have been retained. It does get confusing 
though, doesn't it?

This page tells some of the history of these symbols:

   Earliest uses of mathematical symbols
   http://jeff560.tripod.com/operation.html 

You will find here that the cross was the first multiplication symbol. 
It is retained now primarily for elementary students, since it is more 
distinctive than the other symbols.

The dot was introduced because the cross was too similar to an x, so 
once we get into algebra we tend to drop the cross - until we get into 
vector algebra. Then both "dot product" and "cross product" are 
defined. It was lucky there were two symbols available when vectors 
were invented.

"Juxtaposition," or putting two variables, or a number and a variable, 
next to each other, actually preceded any of the symbols. It 
essentially arises from natural language, where we say "two x's," 
leading us to write "2x." That can't be used when we multiply two 
numbers, unless we put at least one of them in parentheses, so we 
can't easily drop symbols entirely. But using this symbolism whenever 
possible saves a lot of ink.

I would not call parentheses a way to show multiplication, but just a 
way to either hold an expression together so the whole thing is 
multiplied, or to separate two numbers that are being multiplied by 
juxtaposition.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/