Describing Patterns

Date: 10/23/2002 at 17:44:20
From: Danna 
Subject: Vocabulary for math 

What is a pattern? In my math book there isn't a glossary.

Date: 10/23/2002 at 18:36:16
From: Doctor Ian
Subject: Re: Vocabulary for math

Hi Danna,

That's actually a pretty deep question, but for practical purposes, 
we can say that a pattern is any description of a thing that is 
smaller than the thing.  

For example, suppose I give you a string of letters like 

  ajfkduehfujeskoowpdokawwenckjhaehgs

There's no good way for you to describe this except to just list the 
letters. However, suppose I give you a string like 

   ababababababababababababab

You can summarize that by saying it's 

  'ab' repeated 13 times

Some patterns can be trickier than others. For example, 

  abaabbaaabbbaaaabbbbaaaaabbbbb

could be described this way:

  (a repeated n times, b repeated n times) for n = 1, 2, ...

Now, this description is actually longer than the string. But here's 
what makes it a pattern: The description remains the same size, even 
if we continue the string out to a million billion trillion 
repetitions. The same little rule describes the whole string, no 
matter how big the string gets.  And that's what makes it a pattern.

Does this make sense? 

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