What is a Jordan Curve?

Date: 06/07/2006 at 09:34:33
From: Beth
Subject: What is a Jordan Curve

I am trying to explain to a 5th grade class what a Jordan Curve is. 
Is there a simple definition of this?  It is clearly a complex
mathematical concept, but they are curious and I would like to give
them an answer.  :-)

Date: 06/07/2006 at 11:00:21
From: Doctor Peterson
Subject: Re:  What is a Jordan Curve

Hi, Beth.

It isn't really all that complicated; but it is an advanced way of 
thinking about a simple idea!  By clearly defining this simple thing, 
mathematicians can state some surprisingly complex facts about it.

A Jordan curve is a "simple closed curve": that is, a curve that 
starts and ends in the same place, making a closed loop, and that 
doesn't intersect itself.  You can see a complicated-sounding 
definition, and some simple clarifying examples, here:

  Jordan Curve
    http://mathworld.wolfram.com/JordanCurve.html 

See also

  Simple Curve
    http://mathworld.wolfram.com/SimpleCurve.html 
  
  Closed Curve
    http://mathworld.wolfram.com/ClosedCurve.html 

As the examples show, an O, or even a square, is a Jordan curve, but 
a C (not closed) or an 8 (not simple) is not.

If you have any further questions, feel free to write back.


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