Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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

See also

  Simple Curve
  Closed Curve

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
Associated Topics:
Elementary Two-Dimensional Geometry
High School Euclidean/Plane Geometry
Middle School Two-Dimensional Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum