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/ |
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