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Letters for Variables


Date: 11/19/2001 at 10:18:55
From: Spencer Moore
Subject: Variables

Why do we use letters for variables?


Date: 11/19/2001 at 10:51:38
From: Doctor Ian
Subject: Re: Variables

Hi Spencer,

It's much quicker to write

  a = lw

than 

  area(rectangle) = length * width

It's the same reason we use operators instead of words like:

  The area of a rectangle is equal to the product of the 
  length of the rectangle and the width of the rectangle. 

A lot of math involves writing the same equations over and over, with 
small changes. For example:

  a = lw

    = (h - 5)(h + 2)

    = h^2 - 5h + 2h - 10

    = h^2 - 3h - 10

The more you do this, the more you appreciate being able to write what 
you want to say with as few symbols as possible.  

In language, we do a similar thing by using pronouns. That is, it's 
easier to write (and say) 

  Fred and Janet got into their car and drove to their house,
  where their dog was waiting to greet them.

than

  Fred and Janet got into the car belonging to Fred and Janet
  and drove to the house belonging to Fred and Janet, where
  the dog belonging to Fred and Janet was waiting to greet 
  Fred and Janet. 

It's also a lot easier to read! 

The use of letters to represent general numbers goes all the way back 
to Greek antiquity. For information about the beginning uses of 
letters for variables, see Jeff Miller's Web page, Earliest Uses of 
Symbols for Variables:

   http://jeff560.tripod.com/variables.html   

- Doctors Ian and Sarah, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Algebra
Middle School History/Biography

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